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| number = 600 |
| number = 600 |
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| divisor = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 |
| divisor = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 |
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|lang1=[[Armenian numerals|Armenian]]|lang1 symbol=Ո|lang2=[[Hebrew numerals|Hebrew]]|lang2 symbol=<span style="font-size:150%;">ת"ר / ם</span>|lang3=[[Babylonian cuneiform numerals|Babylonian cuneiform]]|lang3 symbol=𒌋|lang4=[[Egyptian numerals|Egyptian hieroglyph]]|lang4 symbol=<span style="font-size:200%;">𓍧</span>}} |
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}} |
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'''600''' ('''six hundred''') is the [[natural number]] following [[500 (number)#590s|599]] and preceding [[#600s|601]]. |
'''600''' ('''six hundred''') is the [[natural number]] following [[500 (number)#590s|599]] and preceding [[#600s|601]]. |
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==Mathematical properties== |
==Mathematical properties== |
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Six hundred is a [[composite number]], an [[abundant number]], a [[pronic number]]<ref name=":0">{{Cite |
Six hundred is a [[composite number]], an [[abundant number]], a [[pronic number]]<ref name=":0">{{Cite OEIS|A002378|Oblong (or promic, pronic, or heteromecic) numbers}}</ref> and a [[Harshad number]]. |
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==Credit and cars== |
==Credit and cars== |
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* In the United States, a [[credit score]] of 600 or below is considered poor, limiting available credit at a normal interest rate |
* In the United States, a [[credit score]] of 600 or below is considered poor, limiting available credit at a normal interest rate |
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* [[NASCAR]] runs 600 advertised miles in the [[Coca-Cola 600]], its longest race |
* [[NASCAR]] runs 600 advertised miles in the [[Coca-Cola 600]], its longest race |
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* The [[Fiat 600]] is a car, the [[SEAT 600]] its Spanish version |
* The [[Fiat 600]] is a car, the [[SEAT 600]] its Spanish version |
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==Integers from 601 to 699== |
==Integers from 601 to 699== |
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===600s=== |
===600s=== |
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* 601 = prime number, [[centered pentagonal number]]<ref name=":1">{{Cite |
* 601 = prime number, [[centered pentagonal number]]<ref name=":1">{{Cite OEIS|A005891|Centered pentagonal numbers}}</ref> |
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* 602 = 2 × 7 × 43, [[nontotient]], [[oeis:A005897|number of cubes of edge length 1 required to make a hollow cube of edge length 11]], area code for [[Phoenix, AZ]] along with [[area code 480|480]] and [[area code 623|623]] |
* 602 = 2 × 7 × 43, [[nontotient]], [[oeis:A005897|number of cubes of edge length 1 required to make a hollow cube of edge length 11]], area code for [[Phoenix, AZ]] along with [[area code 480|480]] and [[area code 623|623]] |
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* 603 = 3<sup>2</sup> × 67, [[Harshad number]], [[oeis:A005043|Riordan number]], [[Area code 603|area code]] for [[New Hampshire]] |
* 603 = 3<sup>2</sup> × 67, [[Harshad number]], [[oeis:A005043|Riordan number]], [[Area code 603|area code]] for [[New Hampshire]] |
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* 604 = 2<sup>2</sup> × 151, [[nontotient]], totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky) |
* 604 = 2<sup>2</sup> × 151, [[nontotient]], totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky) |
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* 605 = 5 × 11<sup>2</sup>, [[Harshad number]], [[oeis:A006002|sum of the nontriangular numbers]] between the two successive [[oeis:A000217|triangular numbers]] 55 and 66, [[oeis:A283877|number of non-isomorphic set-systems of weight 9]] |
* 605 = 5 × 11<sup>2</sup>, [[Harshad number]], [[oeis:A006002|sum of the nontriangular numbers]] between the two successive [[oeis:A000217|triangular numbers]] 55 and 66, [[oeis:A283877|number of non-isomorphic set-systems of weight 9]] |
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* 606 = 2 × 3 × 101, [[sphenic number]], sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109), [[oeis:A111592|admirable number]] |
* 606 = 2 × 3 × 101, [[sphenic number]], sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109), [[oeis:A111592|admirable number]], One of the numbers associated with Christ - ΧϚʹ - see the [[Greek numerals]] [[Isopsephy]] and the reason why other numbers siblings with this one are Beast's numbers. |
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* 607 – prime number, sum of three consecutive primes (197 + 199 + 211), [[Mertens function]](607) = 0, [[balanced prime]],<ref name=":2">{{Cite |
* 607 – prime number, sum of three consecutive primes (197 + 199 + 211), [[Mertens function]](607) = 0, [[balanced prime]],<ref name=":2">{{Cite OEIS|A006562|Balanced primes}}</ref> strictly non-palindromic number,<ref name=":3">{{Cite OEIS|A016038|Strictly non-palindromic numbers}}</ref> [[Mersenne prime]] exponent |
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* 608 = 2<sup>5</sup> × 19, [[Mertens function]](608) = 0, [[nontotient]], [[happy number]], [ |
* 608 = 2<sup>5</sup> × 19, [[Mertens function]](608) = 0, [[nontotient]], [[happy number]], [[oeis:A331452/a331452_18.png|number of regions formed by drawing the line segments connecting any two of the perimeter points of a 3 times 4 grid of squares]]<ref name="OEIS452">{{Cite OEIS|A331452|2=Triangle read by rows: T(n,m) (n >= m >= 1) = number of regions (or cells) formed by drawing the line segments connecting any two of the 2*(m+n) perimeter points of an m X n grid of squares}}</ref> |
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* 609 = 3 × 7 × 29, [[sphenic number]], [[strobogrammatic number]]<ref>{{Cite OEIS| |
* 609 = 3 × 7 × 29, [[sphenic number]], [[strobogrammatic number]]<ref>{{Cite OEIS|A000787|Strobogrammatic numbers}}</ref> |
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===610s=== |
===610s=== |
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* 610 = 2 × 5 × 61, sphenic number |
* 610 = 2 × 5 × 61, sphenic number, [[Fibonacci number]],<ref>{{Cite OEIS|A000045|Fibonacci numbers}}</ref> [[Markov number]],<ref>{{Cite OEIS|A002559|Markoff (or Markov) numbers}}</ref> also a kind of [[610 (telephone)|telephone wall socket]] used in [[Australia]] |
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* 611 = 13 × 47, sum of the three standard board sizes in Go (9<sup>2</sup> + 13<sup>2</sup> + 19<sup>2</sup>), the [[oeis:A232543|611th]] [[oeis:A100683|tribonacci number]] is prime |
* 611 = 13 × 47, sum of the three standard board sizes in Go (9<sup>2</sup> + 13<sup>2</sup> + 19<sup>2</sup>), the [[oeis:A232543|611th]] [[oeis:A100683|tribonacci number]] is prime |
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* 612 = 2<sup>2</sup> × 3<sup>2</sup> × 17, [[Harshad number]], Zuckerman number {{OEIS|id=A007602}}, area code for [[Area code 612|Minneapolis, MN]] |
* 612 = 2<sup>2</sup> × 3<sup>2</sup> × 17, [[Harshad number]], Zuckerman number {{OEIS|id=A007602}}, [[untouchable number]], area code for [[Area code 612|Minneapolis, MN]] |
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⚫ | * [[613 (number)|613]] = prime number, first number of [[prime triple]] (''p'', ''p'' + 4, ''p'' + 6), middle number of [[sexy prime]] triple (''p'' − 6, ''p'', ''p'' + 6). Geometrical numbers: [[Centered square number]] with 18 per side, [[circular number]] of 21 with a square grid and 27 using a triangular grid. Also 17-gonal. Hypotenuse of a right triangle with integral sides, these being 35 and 612. Partitioning: 613 partitions of 47 into non-factor primes, 613 non-squashing partitions into distinct parts of the number 54. Squares: Sum of squares of two consecutive integers, 17 and 18. Additional properties: a [[lucky number]], index of prime Lucas number.<ref name="ReferenceC">{{cite OEIS|A001606|Indices of prime Lucas numbers}}</ref> |
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⚫ | |||
{{Main|613 (number)}} |
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⚫ | |||
⚫ | * 613 = prime number, first number of [[prime triple]] (''p'', ''p'' + 4, ''p'' + 6), middle number of [[sexy prime]] triple (''p'' − 6, ''p'', ''p'' + 6). Geometrical numbers: |
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⚫ | |||
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* 614 = 2 × 307, [[nontotient]], [[Knödel number|2-Knödel number]]. According to Rabbi [[Emil Fackenheim]], the number of Commandments in Judaism should be 614 rather than the traditional 613. |
* 614 = 2 × 307, [[nontotient]], [[Knödel number|2-Knödel number]]. According to Rabbi [[Emil Fackenheim]], the number of Commandments in Judaism should be 614 rather than the traditional 613. |
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* 615 = 3 × 5 × 41, [[sphenic number]] |
* 615 = 3 × 5 × 41, [[sphenic number]] |
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⚫ | * [[616 (number)|616]] = 2<sup>3</sup> × 7 × 11, [[Padovan sequence|Padovan number]], balanced number,<ref>{{cite OEIS|A020492|Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203)}}</ref> an alternative value for the [[Number of the Beast (numerology)|Number of the Beast]] (more commonly accepted to be [[666 (number)|666]]) |
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{{Main|616 (number)}} |
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⚫ | * 616 = 2<sup>3</sup> × 7 × 11, [[Padovan sequence|Padovan number]], balanced number,<ref>{{cite OEIS|A020492|Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203)}}</ref> an alternative value for the [[Number of the Beast (numerology)|Number of the Beast]] (more commonly accepted to be [[666 (number)|666]]) |
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* 617 = prime number, sum of five consecutive primes (109 + 113 + 127 + 131 + 137), [[Chen prime]], [[Eisenstein prime]] with no imaginary part, number of compositions of 17 into distinct parts,<ref>{{cite OEIS|A032020|Number of compositions (ordered partitions) of n into distinct parts|access-date=2022-05-24}}</ref> [[oeis:A006450|prime index prime]], index of prime Lucas number<ref name="ReferenceC"/> |
* 617 = prime number, sum of five consecutive primes (109 + 113 + 127 + 131 + 137), [[Chen prime]], [[Eisenstein prime]] with no imaginary part, number of compositions of 17 into distinct parts,<ref>{{cite OEIS|A032020|Number of compositions (ordered partitions) of n into distinct parts|access-date=2022-05-24}}</ref> [[oeis:A006450|prime index prime]], index of prime Lucas number<ref name="ReferenceC"/> |
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** [[Area codes 617 and 857|Area code 617]], a telephone area code covering the metropolitan Boston area |
** [[Area codes 617 and 857|Area code 617]], a telephone area code covering the metropolitan Boston area |
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* 618 = 2 × 3 × 103, [[sphenic number]], [[oeis:A111592|admirable number]] |
* 618 = 2 × 3 × 103, [[sphenic number]], [[oeis:A111592|admirable number]] |
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* 619 = prime number, [[strobogrammatic prime]],<ref>{{Cite |
* 619 = prime number, [[strobogrammatic prime]],<ref>{{Cite OEIS|A007597|Strobogrammatic primes}}</ref> [[alternating factorial]]<ref>{{Cite OEIS|A005165|Alternating factorials}}</ref> |
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===620s=== |
===620s=== |
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* 620 = 2<sup>2</sup> × 5 × 31, sum of four consecutive primes (149 + 151 + 157 + 163), sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97) |
* 620 = 2<sup>2</sup> × 5 × 31, sum of four consecutive primes (149 + 151 + 157 + 163), sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), the sum of the first 620 primes is itself prime<ref>{{oeis|A013916}}</ref> |
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* 621 = 3<sup>3</sup> × 23, Harshad number, the discriminant of a totally real cubic field<ref>{{cite OEIS|A006832|Discriminants of totally real cubic fields |
* 621 = 3<sup>3</sup> × 23, Harshad number, the discriminant of a totally real cubic field<ref>{{cite OEIS|A006832|Discriminants of totally real cubic fields}}</ref> |
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* 622 = 2 × 311, [[nontotient]], Fine number |
* 622 = 2 × 311, [[nontotient]], Fine number, [[OEIS:A000957|Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree]], it is also the standard diameter of modern road [[bicycle wheel]]s (622 mm, from hook bead to hook bead) |
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* 623 = 7 × 89, number of partitions of 23 into an even number of parts<ref>{{cite OEIS|A027187|Number of partitions of n into an even number of parts |
* 623 = 7 × 89, number of partitions of 23 into an even number of parts<ref>{{cite OEIS|A027187|Number of partitions of n into an even number of parts}}</ref> |
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* 624 = 2<sup>4</sup> × 3 × 13 = [[Jordan's totient function|J<sub>4</sub>(5)]],<ref>{{cite OEIS|A059377|Jordan function J_4(n) |
* 624 = 2<sup>4</sup> × 3 × 13 = [[Jordan's totient function|J<sub>4</sub>(5)]],<ref>{{cite OEIS|A059377|Jordan function J_4(n)}}</ref> sum of a twin prime pair (311 + 313), Harshad number, Zuckerman number |
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* 625 = 25<sup>2</sup> = 5<sup>4</sup>, sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103), [[centered octagonal number]],<ref>{{Cite |
* 625 = 25<sup>2</sup> = 5<sup>4</sup>, sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103), [[centered octagonal number]],<ref>{{Cite OEIS|A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers}}</ref> 1-[[automorphic number]], [[Friedman number]] since 625 = 5<sup>6−2</sup>,<ref name=":4">{{Cite OEIS|A036057|Friedman numbers}}</ref> one of the two three-digit numbers when squared or raised to a higher power that end in the same three digits, the other being [[300_(number)#376|376]] |
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* 626 = 2 × 313, [[nontotient]], [[Knödel number|2-Knödel number]] |
* 626 = 2 × 313, [[nontotient]], [[Knödel number|2-Knödel number]], [[Stitch (Lilo & Stitch)|Stitch]]'s experiment number |
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* 627 = 3 × 11 × 19, sphenic number, number of integer |
* 627 = 3 × 11 × 19, sphenic number, number of [[integer partition]]s of 20,<ref>{{Cite OEIS|A000041|2=a(n) = number of partitions of n}}</ref> [[Smith number]]<ref name=":5">{{Cite OEIS|A006753|Smith numbers}}</ref> |
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* 628 = 2<sup>2</sup> × 157, [[nontotient]], totient sum for first 45 integers |
* 628 = 2<sup>2</sup> × 157, [[nontotient]], totient sum for first 45 integers |
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* 629 = 17 × 37, [[highly cototient number]],<ref name=":6">{{Cite |
* 629 = 17 × 37, [[highly cototient number]],<ref name=":6">{{Cite OEIS|A100827|Highly cototient numbers}}</ref> [[Harshad number]], number of diagonals in a 37-gon<ref name="ReferenceA">{{cite OEIS|A000096|2=a(n) = n*(n+3)/2}}</ref> |
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===630s=== |
===630s=== |
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* 630 = 2 × 3<sup>2</sup> × 5 × 7, sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113), [[triangular number]], [[hexagonal number]],<ref>{{Cite |
* 630 = 2 × 3<sup>2</sup> × 5 × 7, sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113), [[triangular number]], [[hexagonal number]],<ref>{{Cite OEIS|A000384|Hexagonal numbers}}</ref> [[sparsely totient number]],<ref name=":7">{{Cite OEIS|A036913|Sparsely totient numbers}}</ref> Harshad number, balanced number<ref>{{cite OEIS|A020492|Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203)}}</ref> |
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* 631 = [[Cuban prime]] number, [[centered triangular number]],<ref name=":8">{{Cite |
* 631 = [[Cuban prime]] number, [[Lucky prime]], [[centered triangular number]],<ref name=":8">{{Cite OEIS|A005448|Centered triangular numbers}}</ref> [[centered hexagonal number]],<ref>{{Cite OEIS|A003215|Hex (or centered hexagonal) numbers}}</ref> Chen prime, lazy caterer number {{OEIS|id=A000124}} |
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* 632 = 2<sup>3</sup> × 79, [[refactorable number]], number of 13-bead necklaces with 2 colors<ref>{{cite OEIS|A000031|Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n |
* 632 = 2<sup>3</sup> × 79, [[refactorable number]], number of 13-bead necklaces with 2 colors<ref>{{cite OEIS|A000031|Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n}}</ref> |
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* 633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223), [[Blum integer]]; also, in the title of the movie ''[[633 Squadron]]'' |
* 633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223), [[Blum integer]]; also, in the title of the movie ''[[633 Squadron]]'' |
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* 634 = 2 × 317, [[nontotient]], Smith number<ref name=":5" /> |
* 634 = 2 × 317, [[nontotient]], Smith number<ref name=":5" /> |
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* 635 = 5 × 127, sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), Mertens function(635) = 0, number of compositions of 13 into pairwise relatively prime parts<ref>{{cite OEIS|A101268|Number of compositions of n into pairwise relatively prime parts|access-date=2022-05-31}}</ref> |
* 635 = 5 × 127, sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), Mertens function(635) = 0, number of compositions of 13 into pairwise relatively prime parts<ref>{{cite OEIS|A101268|Number of compositions of n into pairwise relatively prime parts|access-date=2022-05-31}}</ref> |
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** "Project 635", the Irtysh River diversion project in China involving a [[Project 635 Dam|dam]] and a [[Irtysh–Karamay–Ürümqi Canal|canal]] |
** "Project 635", the Irtysh River diversion project in China involving a [[Project 635 Dam|dam]] and a [[Irtysh–Karamay–Ürümqi Canal|canal]] |
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* 636 = 2<sup>2</sup> × 3 × 53, sum of ten consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), Smith number,<ref name=":5" /> Mertens function(636) = 0 |
* 636 = 2<sup>2</sup> × 3 × 53, sum of ten consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), Smith number,<ref name=":5" /> Mertens function(636) = 0 |
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* 637 = 7<sup>2</sup> × 13, Mertens function(637) = 0, [[decagonal number]]<ref>{{Cite |
* 637 = 7<sup>2</sup> × 13, Mertens function(637) = 0, [[decagonal number]]<ref>{{Cite OEIS|A001107|10-gonal (or decagonal) numbers}}</ref> |
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* 638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes (151 + 157 + 163 + 167), [[nontotient]], [[centered heptagonal number]]<ref>{{Cite |
* 638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes (151 + 157 + 163 + 167), [[nontotient]], [[centered heptagonal number]]<ref>{{Cite OEIS|A069099|Centered heptagonal numbers}}</ref> |
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* 639 = 3<sup>2</sup> × 71, sum of the first twenty primes, also [[ISO 639]] is the [[International Organization for Standardization|ISO]]'s standard for codes for the representation of [[language]]s |
* 639 = 3<sup>2</sup> × 71, sum of the first twenty primes, also [[ISO 639]] is the [[International Organization for Standardization|ISO]]'s standard for codes for the representation of [[language]]s |
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===640s=== |
===640s=== |
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* 640 = 2<sup>7</sup> × 5, [[Harshad number]], [[refactorable number]], hexadecagonal number,<ref>{{cite OEIS| |
* 640 = 2<sup>7</sup> × 5, [[Harshad number]], [[refactorable number]], hexadecagonal number,<ref>{{cite OEIS|A051868|2=16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6)}}</ref> number of 1's in all partitions of 24 into odd parts,<ref>{{cite OEIS|A036469|Partial sums of A000009 (partitions into distinct parts)}}</ref> number of acres in a square mile |
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* 641 = prime number, [[Sophie Germain prime]],<ref name=":9">{{Cite |
* 641 = prime number, [[Sophie Germain prime]],<ref name=":9">{{Cite OEIS|A005384|Sophie Germain primes}}</ref> factor of [[4294967297 (number)|4294967297]] (the smallest nonprime [[Fermat number]]), Chen prime, Eisenstein prime with no imaginary part, [[Proth prime]]<ref name=":10">{{Cite OEIS|A080076|Proth primes}}</ref> |
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* 642 = 2 × 3 × 107 = 1<sup>4</sup> + 2<sup>4</sup> + 5<sup>4</sup>,<ref>{{cite OEIS| |
* 642 = 2 × 3 × 107 = 1<sup>4</sup> + 2<sup>4</sup> + 5<sup>4</sup>,<ref>{{cite OEIS|A074501|2=a(n) = 1^n + 2^n + 5^n|access-date=2022-05-31}}</ref> [[sphenic number]], [[oeis:A111592|admirable number]] |
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* 643 = prime number, largest prime factor of 123456 |
* 643 = prime number, largest prime factor of 123456 |
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* 644 = 2<sup>2</sup> × 7 × 23, [[nontotient]], [[Perrin number]],<ref>{{Cite web|url=https://oeis.org/A001608|title=Sloane's A001608 : Perrin sequence|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> Harshad number, common [[umask]], [[oeis:A111592|admirable number]] |
* 644 = 2<sup>2</sup> × 7 × 23, [[nontotient]], [[Perrin number]],<ref>{{Cite web|url=https://oeis.org/A001608|title=Sloane's A001608 : Perrin sequence|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> Harshad number, common [[umask]], [[oeis:A111592|admirable number]] |
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* 645 = 3 × 5 × 43, sphenic number, [[octagonal number]], Smith number,<ref name=":5" /> [[Fermat pseudoprime]] to base 2,<ref>{{Cite |
* 645 = 3 × 5 × 43, sphenic number, [[octagonal number]], Smith number,<ref name=":5" /> [[Fermat pseudoprime]] to base 2,<ref>{{Cite OEIS|A001567|Fermat pseudoprimes to base 2}}</ref> Harshad number |
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* 646 = 2 × 17 × 19, sphenic number, also [[ISO 646]] is the ISO's standard for international 7-bit variants of [[ASCII]], number of permutations of length 7 without rising or falling successions<ref>{{cite OEIS|A002464|Hertzsprung's problem: ways to arrange n non-attacking kings on an n X n board, with 1 in each row and column. Also number of permutations of length n without rising or falling successions |
* 646 = 2 × 17 × 19, sphenic number, also [[ISO 646]] is the ISO's standard for international 7-bit variants of [[ASCII]], number of permutations of length 7 without rising or falling successions<ref>{{cite OEIS|A002464|Hertzsprung's problem: ways to arrange n non-attacking kings on an n X n board, with 1 in each row and column. Also number of permutations of length n without rising or falling successions}}</ref> |
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* 647 = prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, 3<sup>647</sup> - 2<sup>647</sup> is prime<ref>{{cite OEIS|A057468|Numbers k such that 3^k - 2^k is prime |
* 647 = prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, 3<sup>647</sup> - 2<sup>647</sup> is prime<ref>{{cite OEIS|A057468|Numbers k such that 3^k - 2^k is prime}}</ref> |
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* 648 = 2<sup>3</sup> × 3<sup>4</sup> = [https://oeis.org/A331452/a331452_32.png A331452(7, 1)],<ref |
* 648 = 2<sup>3</sup> × 3<sup>4</sup> = [https://oeis.org/A331452/a331452_32.png A331452(7, 1)],<ref name="OEIS452" /> Harshad number, [[Achilles number]], area of a square with diagonal 36<ref name = "area of a square with diagonal 2n">{{cite OEIS|A001105|2=a(n) = 2*n^2}}</ref> |
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* 649 = 11 × 59, [[Blum integer]] |
* 649 = 11 × 59, [[Blum integer]] |
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===650s=== |
===650s=== |
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* 650 = 2 × 5<sup>2</sup> × 13, [[primitive abundant number]],<ref>{{Cite |
* 650 = 2 × 5<sup>2</sup> × 13, [[primitive abundant number]],<ref>{{Cite OEIS|A071395|Primitive abundant numbers}}</ref> [[square pyramidal number]],<ref>{{Cite OEIS|A000330|Square pyramidal numbers}}</ref> pronic number,<ref name=":0" /> [[nontotient]], totient sum for first 46 integers; (other fields) {{anchor|650 other fields}}the number of seats in the [[House of Commons of the United Kingdom]], [[oeis:A111592|admirable number]] |
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* 651 = 3 × 7 × 31, sphenic number, [[pentagonal number]],<ref>{{Cite |
* 651 = 3 × 7 × 31, sphenic number, [[pentagonal number]],<ref>{{Cite OEIS|A000326|Pentagonal numbers}}</ref> [[nonagonal number]]<ref>{{Cite OEIS|A001106|9-gonal (or enneagonal or nonagonal) numbers}}</ref> |
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* 652 = 2<sup>2</sup> × 163, maximal number of regions by drawing 26 circles<ref>{{cite OEIS| |
* 652 = 2<sup>2</sup> × 163, maximal number of regions by drawing 26 circles<ref>{{cite OEIS|A014206|2=a(n) = n^2 + n + 2}}</ref> |
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* 653 = prime number, Sophie Germain prime,<ref name=":9" /> balanced prime,<ref name=":2" /> Chen prime, Eisenstein prime with no imaginary part |
* 653 = prime number, Sophie Germain prime,<ref name=":9" /> balanced prime,<ref name=":2" /> Chen prime, Eisenstein prime with no imaginary part |
||
* 654 = 2 × 3 × 109, sphenic number, [[nontotient]], Smith number,<ref name=":5" /> [[oeis:A111592|admirable number]] |
* 654 = 2 × 3 × 109, sphenic number, [[nontotient]], Smith number,<ref name=":5" /> [[oeis:A111592|admirable number]] |
||
* 655 = 5 × 131, number of toothpicks after 20 stages in a three-dimensional grid<ref>{{cite OEIS|A160160|Toothpick sequence in the three-dimensional grid |
* 655 = 5 × 131, number of toothpicks after 20 stages in a three-dimensional grid<ref>{{cite OEIS|A160160|Toothpick sequence in the three-dimensional grid}}</ref> |
||
* 656 = 2<sup>4</sup> × 41 = <math>\lfloor \frac{3^{16}}{2^{16}} \rfloor</math> |
* 656 = 2<sup>4</sup> × 41 = <math>\lfloor \frac{3^{16}}{2^{16}} \rfloor</math>,<ref>{{cite OEIS|A002379|2=a(n) = floor(3^n / 2^n)}}</ref> in [[Judaism]], 656 is the number of times that [[Jerusalem]] is mentioned in the [[Hebrew Bible]] or [[Old Testament]] |
||
* 657 = 3<sup>2</sup> × 73, the largest known number not of the form ''a''<sup>2</sup>+''s'' with ''s'' a [[semiprime]] |
* 657 = 3<sup>2</sup> × 73, the largest known number not of the form ''a''<sup>2</sup>+''s'' with ''s'' a [[semiprime]] |
||
* 658 = 2 × 7 × 47, [[sphenic number]], [[untouchable number]] |
* 658 = 2 × 7 × 47, [[sphenic number]], [[untouchable number]] |
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Line 100: | Line 96: | ||
===660s=== |
===660s=== |
||
* 660 = 2<sup>2</sup> × 3 × 5 × 11 |
* 660 = 2<sup>2</sup> × 3 × 5 × 11 |
||
**Sum of four consecutive primes (157 + 163 + 167 + 173) |
**Sum of four consecutive primes (157 + 163 + 167 + 173) |
||
**Sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127) |
**Sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127) |
||
**Sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101) |
**Sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101) |
||
**Sparsely totient number |
**Sparsely totient number<ref name=":7" /> |
||
**Sum of 11th row when writing the natural numbers as a triangle.<ref>{{cite OEIS| |
**Sum of 11th row when writing the natural numbers as a triangle.<ref>{{cite OEIS|A027480|2=a(n) = n*(n+1)*(n+2)/2}}</ref> |
||
**[[Harshad number]]. |
**[[Harshad number]]. |
||
* 661 = prime number |
* 661 = prime number |
||
**Sum of three consecutive primes (211 + 223 + 227) |
**Sum of three consecutive primes (211 + 223 + 227) |
||
**Mertens function sets new low of −11 which stands until 665 |
**Mertens function sets new low of −11 which stands until 665 |
||
**[[Pentagram]] number of the form <math>5n^{2}-5n+1</math> |
**[[Pentagram]] number of the form <math>5n^{2}-5n+1</math> |
||
**[[Hexagram]] number of the form <math>6n^{2}-6n+1</math> i.e. a [[star number]] |
**[[Hexagram]] number of the form <math>6n^{2}-6n+1</math> i.e. a [[star number]] |
||
* 662 = 2 × 331, [[nontotient]], member of [[Mian–Chowla sequence]]<ref>{{Cite |
* 662 = 2 × 331, [[nontotient]], member of [[Mian–Chowla sequence]]<ref>{{Cite OEIS|A005282|Mian-Chowla sequence}}</ref> |
||
* 663 = 3 × 13 × 17, [[sphenic number]], Smith number<ref name=":5" /> |
* 663 = 3 × 13 × 17, [[sphenic number]], Smith number<ref name=":5" /> |
||
* 664 = 2<sup>3</sup> × 83, [[refactorable number]], number of knapsack partitions of 33<ref>{{cite OEIS|A108917|Number of knapsack partitions of n |
* 664 = 2<sup>3</sup> × 83, [[refactorable number]], number of knapsack partitions of 33<ref>{{cite OEIS|A108917|Number of knapsack partitions of n}}</ref> |
||
**Telephone [[area code 664|area code for Montserrat]] |
**Telephone [[area code 664|area code for Montserrat]] |
||
**[[Area code 664 (Mexico)|Area code for Tijuana]] within Mexico |
**[[Area code 664 (Mexico)|Area code for Tijuana]] within Mexico |
||
**Model number for the [[Amstrad |
**Model number for the [[Amstrad CPC 664]] home computer |
||
* 665 = 5 × 7 × 19, [[sphenic number]], Mertens function sets new low of −12 which stands until 1105, number of diagonals in a 38-gon<ref name="ReferenceA"/> |
* 665 = 5 × 7 × 19, [[sphenic number]], Mertens function sets new low of −12 which stands until 1105, number of diagonals in a 38-gon<ref name="ReferenceA"/> |
||
* [[666 (number)|666]] = 2 × 3<sup>2</sup> × 37, [[Harshad number]], [[repdigit]] |
* [[666 (number)|666]] = 2 × 3<sup>2</sup> × 37, 36th [[triangular number]], [[Harshad number]], [[repdigit]] |
||
* 667 = 23 × 29, lazy caterer number {{OEIS|id=A000124}} |
* 667 = 23 × 29, lazy caterer number {{OEIS|id=A000124}} |
||
* 668 = 2<sup>2</sup> × 167, [[nontotient]] |
* 668 = 2<sup>2</sup> × 167, [[nontotient]] |
||
* 669 = 3 × 223, [[ |
* 669 = 3 × 223, [[Blum integer]] |
||
===670s=== |
===670s=== |
||
* 670 = 2 × 5 × 67, sphenic number, [[octahedral number]],<ref>{{Cite |
* 670 = 2 × 5 × 67, sphenic number, [[octahedral number]],<ref>{{Cite OEIS|A005900|Octahedral numbers}}</ref> [[nontotient]] |
||
* 671 = 11 × 61. This number is the [[magic constant]] of ''n''×''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 11. |
* 671 = 11 × 61. This number is the [[magic constant]] of ''n''×''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 11. |
||
* 672 = 2<sup>5</sup> × 3 × 7, [[harmonic divisor number]],<ref>{{Cite |
* 672 = 2<sup>5</sup> × 3 × 7, [[harmonic divisor number]],<ref>{{Cite OEIS|A001599|Harmonic or Ore numbers}}</ref> Zuckerman number, [[oeis:A111592|admirable number]] |
||
* 673 = prime number, Proth prime<ref name=":10" /> |
* 673 = prime number, lucky prime, Proth prime<ref name=":10" /> |
||
* 674 = 2 × 337, [[nontotient]], [[Knödel number|2-Knödel number]] |
* 674 = 2 × 337, [[nontotient]], [[Knödel number|2-Knödel number]] |
||
* 675 = 3<sup>3</sup> × 5<sup>2</sup>, [[Achilles number]] |
* 675 = 3<sup>3</sup> × 5<sup>2</sup>, [[Achilles number]] |
||
* 676 = 2<sup>2</sup> × 13<sup>2</sup> = 26<sup>2</sup>, palindromic square |
* 676 = 2<sup>2</sup> × 13<sup>2</sup> = 26<sup>2</sup>, palindromic square |
||
* 677 = prime number, Chen prime, Eisenstein prime with no imaginary part, number of non-isomorphic self-dual multiset partitions of weight 10<ref>{{cite OEIS|A316983|Number of non-isomorphic self-dual multiset partitions of weight n |
* 677 = prime number, Chen prime, Eisenstein prime with no imaginary part, number of non-isomorphic self-dual multiset partitions of weight 10<ref>{{cite OEIS|A316983|Number of non-isomorphic self-dual multiset partitions of weight n}}</ref> |
||
* 678 = 2 × 3 × 113, sphenic number, [[nontotient]], number of surface points of an octahedron with side length 13,<ref>{{cite OEIS|A005899|Number of points on surface of octahedron with side n|access-date=2022-05-31}}</ref> [[oeis:A111592|admirable number]] |
* 678 = 2 × 3 × 113, sphenic number, [[nontotient]], number of surface points of an octahedron with side length 13,<ref>{{cite OEIS|A005899|Number of points on surface of octahedron with side n|access-date=2022-05-31}}</ref> [[oeis:A111592|admirable number]] |
||
* 679 = 7 × 97, sum of three consecutive primes (223 + 227 + 229), sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), smallest number of multiplicative persistence 5<ref>{{cite OEIS|A003001|Smallest number of multiplicative persistence n|access-date=2022-05-31}}</ref> |
* 679 = 7 × 97, sum of three consecutive primes (223 + 227 + 229), sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), smallest number of multiplicative persistence 5<ref>{{cite OEIS|A003001|Smallest number of multiplicative persistence n|access-date=2022-05-31}}</ref> |
||
===680s=== |
===680s=== |
||
* 680 = 2<sup>3</sup> × 5 × 17, [[tetrahedral number]],<ref>{{Cite |
* 680 = 2<sup>3</sup> × 5 × 17, [[tetrahedral number]],<ref>{{Cite OEIS|A000292|Tetrahedral numbers|access-date=2016-06-11}}</ref> [[nontotient]] |
||
* 681 = 3 × 227, centered pentagonal number<ref name=":1" /> |
* 681 = 3 × 227, centered pentagonal number<ref name=":1" /> |
||
* 682 = 2 × 11 × 31, sphenic number, sum of four consecutive primes (163 + 167 + 173 + 179), sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), number of moves to solve the Norwegian puzzle [http://oeis.org/A000975/a000975.jpg strikketoy] |
* 682 = 2 × 11 × 31, sphenic number, sum of four consecutive primes (163 + 167 + 173 + 179), sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), number of moves to solve the Norwegian puzzle [http://oeis.org/A000975/a000975.jpg strikketoy]<ref>{{cite OEIS|A000975|Lichtenberg sequence|access-date=2022-05-31}}</ref> |
||
* 683 = prime number, Sophie Germain prime,<ref name=":9" /> sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, [[Wagstaff prime]]<ref>{{Cite |
* 683 = prime number, Sophie Germain prime,<ref name=":9" /> sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, [[Wagstaff prime]]<ref>{{Cite OEIS|A000979|Wagstaff primes|access-date=2016-06-11}}</ref> |
||
* 684 = 2<sup>2</sup> × 3<sup>2</sup> × 19, Harshad number, number of graphical forest partitions of 32<ref>{{cite OEIS| |
* 684 = 2<sup>2</sup> × 3<sup>2</sup> × 19, Harshad number, number of graphical forest partitions of 32<ref>{{cite OEIS|A000070|2=a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041)|access-date=2022-05-31}}</ref> |
||
* 685 = 5 × 137, centered square number<ref>{{Cite |
* 685 = 5 × 137, centered square number<ref>{{Cite OEIS|A001844|Centered square numbers|access-date=2016-06-11}}</ref> |
||
* 686 = 2 × 7<sup>3</sup>, [[nontotient]], number of multigraphs on infinite set of nodes with 7 edges<ref>{{cite OEIS|A050535|Number of multigraphs on infinite set of nodes with n edges|access-date=2022-05-31}}</ref> |
* 686 = 2 × 7<sup>3</sup>, [[nontotient]], number of multigraphs on infinite set of nodes with 7 edges<ref>{{cite OEIS|A050535|Number of multigraphs on infinite set of nodes with n edges|access-date=2022-05-31}}</ref> |
||
* 687 = 3 × 229, 687 days to orbit the Sun ([[Mars]]) [[Knödel number|D-number]]<ref name="ReferenceB">{{cite OEIS| |
* 687 = 3 × 229, 687 days to orbit the Sun ([[Mars]]) [[Knödel number|D-number]]<ref name="ReferenceB">{{cite OEIS|A033553|2=3-Knödel numbers or D-numbers: numbers n > 3 such that n divides k^(n-2)-k for all k with gcd(k, n) = 1|access-date=2022-05-31}}</ref> |
||
* 688 = 2<sup>4</sup> × 43, Friedman number since 688 = 8 × 86,<ref name=":4" /> 2-[[automorphic number]]<ref>{{Cite OEIS|A030984|2-automorphic numbers|access-date=2021-09-01}}</ref> |
* 688 = 2<sup>4</sup> × 43, Friedman number since 688 = 8 × 86,<ref name=":4" /> 2-[[automorphic number]]<ref>{{Cite OEIS|A030984|2-automorphic numbers|access-date=2021-09-01}}</ref> |
||
* 689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109). [[Strobogrammatic number]]<ref>{{Cite |
* 689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109). [[Strobogrammatic number]]<ref>{{Cite OEIS|A000787|Strobogrammatic numbers}}</ref> |
||
===690s=== |
===690s=== |
||
* 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number,<ref name=":7" /> Smith number,<ref name=":5" /> Harshad number |
* 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number,<ref name=":7" /> Smith number,<ref name=":5" /> Harshad number |
||
** [[ISO 690]] is the ISO's standard for bibliographic references |
** [[ISO 690]] is the ISO's standard for bibliographic references |
||
* 691 = prime number, (negative) numerator of the [[Bernoulli number]] ''B''<sub>12</sub> = -691/2730. [[Ramanujan's tau function]] τ and the [[divisor function]] σ<sub>11</sub> are related by the remarkable congruence |
* 691 = prime number, (negative) numerator of the [[Bernoulli number]] ''B''<sub>12</sub> = -691/2730. [[Ramanujan's tau function]] τ and the [[divisor function]] σ<sub>11</sub> are related by the remarkable congruence τ(''n'') ≡ σ<sub>11</sub>(''n'') (mod 691). |
||
** In number theory, 691 is a "marker" (similar to the radioactive markers in biology): whenever it appears in a computation, one can be sure that Bernoulli numbers are involved. |
** In number theory, 691 is a "marker" (similar to the radioactive markers in biology): whenever it appears in a computation, one can be sure that Bernoulli numbers are involved. |
||
* 692 = 2<sup>2</sup> × 173, number of partitions of 48 into powers of 2<ref>{{cite OEIS|A000123|Number of binary partitions: number of partitions of 2n into powers of 2|access-date=2022-05-31}}</ref> |
* 692 = 2<sup>2</sup> × 173, number of partitions of 48 into powers of 2<ref>{{cite OEIS|A000123|Number of binary partitions: number of partitions of 2n into powers of 2|access-date=2022-05-31}}</ref> |
||
* [[693 (number)|693]] = 3<sup>2</sup> × 7 × 11, triangular matchstick number,<ref>{{cite OEIS| |
* [[693 (number)|693]] = 3<sup>2</sup> × 7 × 11, triangular matchstick number,<ref>{{cite OEIS|A045943|2=Triangular matchstick numbers: a(n) = 3*n*(n+1)/2|access-date=2022-05-31}}</ref> the number of sections in [[Ludwig Wittgenstein]]'s ''[[Philosophical Investigations]]''. |
||
* 694 = 2 × 347, centered triangular number,<ref name=":8" /> [[nontotient]] |
* 694 = 2 × 347, centered triangular number,<ref name=":8" /> [[nontotient]], smallest pandigital number in base 5.<ref>{{cite OEIS|A049363|2=a(1) = 1; for n > 1, smallest digitally balanced number in base n}}</ref> |
||
* 695 = 5 × 139, 695!! + 2 is prime.<ref>{{cite OEIS|A076185|Numbers n such that n!! + 2 is prime|access-date=2022-05-31}}</ref> |
* 695 = 5 × 139, 695!! + 2 is prime.<ref>{{cite OEIS|A076185|Numbers n such that n!! + 2 is prime|access-date=2022-05-31}}</ref> |
||
* 696 = 2<sup>3</sup> × 3 × 29, sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers, trails of length 9 on honeycomb lattice |
* 696 = 2<sup>3</sup> × 3 × 29, sum of a twin prime (347 + 349) sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers, trails of length 9 on honeycomb lattice<ref>{{cite OEIS|A006851|Trails of length n on honeycomb lattice|access-date=2022-05-18}}</ref> |
||
* 697 = 17 × 41, [[cake number]]; the number of sides of Colorado<ref>{{Cite web|url=https://bigthink.com/strange-maps/colorado-is-not-a-rectangle|title=Colorado is a rectangle? Think again|date=23 January 2023 }}</ref> |
* 697 = 17 × 41, [[cake number]]; the number of sides of Colorado<ref>{{Cite web|url=https://bigthink.com/strange-maps/colorado-is-not-a-rectangle|title=Colorado is a rectangle? Think again|date=23 January 2023 }}</ref> |
||
* 698 = 2 × 349, [[nontotient]], sum of squares of two primes<ref>{{cite OEIS|A045636|Numbers of the form p^2 + q^2, with p and q primes |
* 698 = 2 × 349, [[nontotient]], sum of squares of two primes<ref>{{cite OEIS|A045636|Numbers of the form p^2 + q^2, with p and q primes}}</ref> |
||
* 699 = 3 × 233, [[Knödel number|D-number]]<ref name="ReferenceB"/> |
* 699 = 3 × 233, [[Knödel number|D-number]]<ref name="ReferenceB"/> |
||
== |
== $10000 (23606583 == |
||
<references /> |
<references /> |
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Latest revision as of 03:54, 2 September 2024
| ||||
---|---|---|---|---|
Cardinal | six hundred | |||
Ordinal | 600th (six hundredth) | |||
Factorization | 23 × 3 × 52 | |||
Divisors | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 | |||
Greek numeral | Χ´ | |||
Roman numeral | DC | |||
Binary | 10010110002 | |||
Ternary | 2110203 | |||
Senary | 24406 | |||
Octal | 11308 | |||
Duodecimal | 42012 | |||
Hexadecimal | 25816 | |||
Armenian | Ո | |||
Hebrew | ת"ר / ם | |||
Babylonian cuneiform | 𒌋 | |||
Egyptian hieroglyph | 𓍧 |
600 (six hundred) is the natural number following 599 and preceding 601.
Mathematical properties
[edit]Six hundred is a composite number, an abundant number, a pronic number[1] and a Harshad number.
Credit and cars
[edit]- In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate
- NASCAR runs 600 advertised miles in the Coca-Cola 600, its longest race
- The Fiat 600 is a car, the SEAT 600 its Spanish version
Integers from 601 to 699
[edit]600s
[edit]- 601 = prime number, centered pentagonal number[2]
- 602 = 2 × 7 × 43, nontotient, number of cubes of edge length 1 required to make a hollow cube of edge length 11, area code for Phoenix, AZ along with 480 and 623
- 603 = 32 × 67, Harshad number, Riordan number, area code for New Hampshire
- 604 = 22 × 151, nontotient, totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky)
- 605 = 5 × 112, Harshad number, sum of the nontriangular numbers between the two successive triangular numbers 55 and 66, number of non-isomorphic set-systems of weight 9
- 606 = 2 × 3 × 101, sphenic number, sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109), admirable number, One of the numbers associated with Christ - ΧϚʹ - see the Greek numerals Isopsephy and the reason why other numbers siblings with this one are Beast's numbers.
- 607 – prime number, sum of three consecutive primes (197 + 199 + 211), Mertens function(607) = 0, balanced prime,[3] strictly non-palindromic number,[4] Mersenne prime exponent
- 608 = 25 × 19, Mertens function(608) = 0, nontotient, happy number, number of regions formed by drawing the line segments connecting any two of the perimeter points of a 3 times 4 grid of squares[5]
- 609 = 3 × 7 × 29, sphenic number, strobogrammatic number[6]
610s
[edit]- 610 = 2 × 5 × 61, sphenic number, Fibonacci number,[7] Markov number,[8] also a kind of telephone wall socket used in Australia
- 611 = 13 × 47, sum of the three standard board sizes in Go (92 + 132 + 192), the 611th tribonacci number is prime
- 612 = 22 × 32 × 17, Harshad number, Zuckerman number (sequence A007602 in the OEIS), untouchable number, area code for Minneapolis, MN
- 613 = prime number, first number of prime triple (p, p + 4, p + 6), middle number of sexy prime triple (p − 6, p, p + 6). Geometrical numbers: Centered square number with 18 per side, circular number of 21 with a square grid and 27 using a triangular grid. Also 17-gonal. Hypotenuse of a right triangle with integral sides, these being 35 and 612. Partitioning: 613 partitions of 47 into non-factor primes, 613 non-squashing partitions into distinct parts of the number 54. Squares: Sum of squares of two consecutive integers, 17 and 18. Additional properties: a lucky number, index of prime Lucas number.[9]
- In Judaism the number 613 is very significant, as its metaphysics, the Kabbalah, views every complete entity as divisible into 613 parts: 613 parts of every Sefirah; 613 mitzvot, or divine Commandments in the Torah; 613 parts of the human body.
- The number 613 hangs from the rafters at Madison Square Garden in honor of New York Knicks coach Red Holzman's 613 victories
- 614 = 2 × 307, nontotient, 2-Knödel number. According to Rabbi Emil Fackenheim, the number of Commandments in Judaism should be 614 rather than the traditional 613.
- 615 = 3 × 5 × 41, sphenic number
- 616 = 23 × 7 × 11, Padovan number, balanced number,[10] an alternative value for the Number of the Beast (more commonly accepted to be 666)
- 617 = prime number, sum of five consecutive primes (109 + 113 + 127 + 131 + 137), Chen prime, Eisenstein prime with no imaginary part, number of compositions of 17 into distinct parts,[11] prime index prime, index of prime Lucas number[9]
- Area code 617, a telephone area code covering the metropolitan Boston area
- 618 = 2 × 3 × 103, sphenic number, admirable number
- 619 = prime number, strobogrammatic prime,[12] alternating factorial[13]
620s
[edit]- 620 = 22 × 5 × 31, sum of four consecutive primes (149 + 151 + 157 + 163), sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), the sum of the first 620 primes is itself prime[14]
- 621 = 33 × 23, Harshad number, the discriminant of a totally real cubic field[15]
- 622 = 2 × 311, nontotient, Fine number, Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree, it is also the standard diameter of modern road bicycle wheels (622 mm, from hook bead to hook bead)
- 623 = 7 × 89, number of partitions of 23 into an even number of parts[16]
- 624 = 24 × 3 × 13 = J4(5),[17] sum of a twin prime pair (311 + 313), Harshad number, Zuckerman number
- 625 = 252 = 54, sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103), centered octagonal number,[18] 1-automorphic number, Friedman number since 625 = 56−2,[19] one of the two three-digit numbers when squared or raised to a higher power that end in the same three digits, the other being 376
- 626 = 2 × 313, nontotient, 2-Knödel number, Stitch's experiment number
- 627 = 3 × 11 × 19, sphenic number, number of integer partitions of 20,[20] Smith number[21]
- 628 = 22 × 157, nontotient, totient sum for first 45 integers
- 629 = 17 × 37, highly cototient number,[22] Harshad number, number of diagonals in a 37-gon[23]
630s
[edit]- 630 = 2 × 32 × 5 × 7, sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113), triangular number, hexagonal number,[24] sparsely totient number,[25] Harshad number, balanced number[26]
- 631 = Cuban prime number, Lucky prime, centered triangular number,[27] centered hexagonal number,[28] Chen prime, lazy caterer number (sequence A000124 in the OEIS)
- 632 = 23 × 79, refactorable number, number of 13-bead necklaces with 2 colors[29]
- 633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223), Blum integer; also, in the title of the movie 633 Squadron
- 634 = 2 × 317, nontotient, Smith number[21]
- 635 = 5 × 127, sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), Mertens function(635) = 0, number of compositions of 13 into pairwise relatively prime parts[30]
- 636 = 22 × 3 × 53, sum of ten consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), Smith number,[21] Mertens function(636) = 0
- 637 = 72 × 13, Mertens function(637) = 0, decagonal number[31]
- 638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes (151 + 157 + 163 + 167), nontotient, centered heptagonal number[32]
- 639 = 32 × 71, sum of the first twenty primes, also ISO 639 is the ISO's standard for codes for the representation of languages
640s
[edit]- 640 = 27 × 5, Harshad number, refactorable number, hexadecagonal number,[33] number of 1's in all partitions of 24 into odd parts,[34] number of acres in a square mile
- 641 = prime number, Sophie Germain prime,[35] factor of 4294967297 (the smallest nonprime Fermat number), Chen prime, Eisenstein prime with no imaginary part, Proth prime[36]
- 642 = 2 × 3 × 107 = 14 + 24 + 54,[37] sphenic number, admirable number
- 643 = prime number, largest prime factor of 123456
- 644 = 22 × 7 × 23, nontotient, Perrin number,[38] Harshad number, common umask, admirable number
- 645 = 3 × 5 × 43, sphenic number, octagonal number, Smith number,[21] Fermat pseudoprime to base 2,[39] Harshad number
- 646 = 2 × 17 × 19, sphenic number, also ISO 646 is the ISO's standard for international 7-bit variants of ASCII, number of permutations of length 7 without rising or falling successions[40]
- 647 = prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, 3647 - 2647 is prime[41]
- 648 = 23 × 34 = A331452(7, 1),[5] Harshad number, Achilles number, area of a square with diagonal 36[42]
- 649 = 11 × 59, Blum integer
650s
[edit]- 650 = 2 × 52 × 13, primitive abundant number,[43] square pyramidal number,[44] pronic number,[1] nontotient, totient sum for first 46 integers; (other fields) the number of seats in the House of Commons of the United Kingdom, admirable number
- 651 = 3 × 7 × 31, sphenic number, pentagonal number,[45] nonagonal number[46]
- 652 = 22 × 163, maximal number of regions by drawing 26 circles[47]
- 653 = prime number, Sophie Germain prime,[35] balanced prime,[3] Chen prime, Eisenstein prime with no imaginary part
- 654 = 2 × 3 × 109, sphenic number, nontotient, Smith number,[21] admirable number
- 655 = 5 × 131, number of toothpicks after 20 stages in a three-dimensional grid[48]
- 656 = 24 × 41 = ,[49] in Judaism, 656 is the number of times that Jerusalem is mentioned in the Hebrew Bible oder Old Testament
- 657 = 32 × 73, the largest known number not of the form a2+s with s a semiprime
- 658 = 2 × 7 × 47, sphenic number, untouchable number
- 659 = prime number, Sophie Germain prime,[35] sum of seven consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107), Chen prime, Mertens function sets new low of −10 which stands until 661, highly cototient number,[22] Eisenstein prime with no imaginary part, strictly non-palindromic number[4]
660s
[edit]- 660 = 22 × 3 × 5 × 11
- Sum of four consecutive primes (157 + 163 + 167 + 173)
- Sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127)
- Sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101)
- Sparsely totient number[25]
- Sum of 11th row when writing the natural numbers as a triangle.[50]
- Harshad number.
- 661 = prime number
- Sum of three consecutive primes (211 + 223 + 227)
- Mertens function sets new low of −11 which stands until 665
- Pentagram number of the form
- Hexagram number of the form i.e. a star number
- 662 = 2 × 331, nontotient, member of Mian–Chowla sequence[51]
- 663 = 3 × 13 × 17, sphenic number, Smith number[21]
- 664 = 23 × 83, refactorable number, number of knapsack partitions of 33[52]
- Telephone area code for Montserrat
- Area code for Tijuana within Mexico
- Model number for the Amstrad CPC 664 home computer
- 665 = 5 × 7 × 19, sphenic number, Mertens function sets new low of −12 which stands until 1105, number of diagonals in a 38-gon[23]
- 666 = 2 × 32 × 37, 36th triangular number, Harshad number, repdigit
- 667 = 23 × 29, lazy caterer number (sequence A000124 in the OEIS)
- 668 = 22 × 167, nontotient
- 669 = 3 × 223, Blum integer
670s
[edit]- 670 = 2 × 5 × 67, sphenic number, octahedral number,[53] nontotient
- 671 = 11 × 61. This number is the magic constant of n×n normal magic square and n-queens problem for n = 11.
- 672 = 25 × 3 × 7, harmonic divisor number,[54] Zuckerman number, admirable number
- 673 = prime number, lucky prime, Proth prime[36]
- 674 = 2 × 337, nontotient, 2-Knödel number
- 675 = 33 × 52, Achilles number
- 676 = 22 × 132 = 262, palindromic square
- 677 = prime number, Chen prime, Eisenstein prime with no imaginary part, number of non-isomorphic self-dual multiset partitions of weight 10[55]
- 678 = 2 × 3 × 113, sphenic number, nontotient, number of surface points of an octahedron with side length 13,[56] admirable number
- 679 = 7 × 97, sum of three consecutive primes (223 + 227 + 229), sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), smallest number of multiplicative persistence 5[57]
680s
[edit]- 680 = 23 × 5 × 17, tetrahedral number,[58] nontotient
- 681 = 3 × 227, centered pentagonal number[2]
- 682 = 2 × 11 × 31, sphenic number, sum of four consecutive primes (163 + 167 + 173 + 179), sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), number of moves to solve the Norwegian puzzle strikketoy[59]
- 683 = prime number, Sophie Germain prime,[35] sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, Wagstaff prime[60]
- 684 = 22 × 32 × 19, Harshad number, number of graphical forest partitions of 32[61]
- 685 = 5 × 137, centered square number[62]
- 686 = 2 × 73, nontotient, number of multigraphs on infinite set of nodes with 7 edges[63]
- 687 = 3 × 229, 687 days to orbit the Sun (Mars) D-number[64]
- 688 = 24 × 43, Friedman number since 688 = 8 × 86,[19] 2-automorphic number[65]
- 689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109). Strobogrammatic number[66]
690s
[edit]- 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number,[25] Smith number,[21] Harshad number
- ISO 690 is the ISO's standard for bibliographic references
- 691 = prime number, (negative) numerator of the Bernoulli number B12 = -691/2730. Ramanujan's tau function τ and the divisor function σ11 are related by the remarkable congruence τ(n) ≡ σ11(n) (mod 691).
- In number theory, 691 is a "marker" (similar to the radioactive markers in biology): whenever it appears in a computation, one can be sure that Bernoulli numbers are involved.
- 692 = 22 × 173, number of partitions of 48 into powers of 2[67]
- 693 = 32 × 7 × 11, triangular matchstick number,[68] the number of sections in Ludwig Wittgenstein's Philosophical Investigations.
- 694 = 2 × 347, centered triangular number,[27] nontotient, smallest pandigital number in base 5.[69]
- 695 = 5 × 139, 695!! + 2 is prime.[70]
- 696 = 23 × 3 × 29, sum of a twin prime (347 + 349) sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers, trails of length 9 on honeycomb lattice[71]
- 697 = 17 × 41, cake number; the number of sides of Colorado[72]
- 698 = 2 × 349, nontotient, sum of squares of two primes[73]
- 699 = 3 × 233, D-number[64]
$10000 (23606583
[edit]- ^ a b Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A331452 (Triangle read by rows: T(n,m) (n >= m >= 1) = number of regions (or cells) formed by drawing the line segments connecting any two of the 2*(m+n) perimeter points of an m X n grid of squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
- ^ Sloane, N. J. A. (ed.). "Sequence A007597 (Strobogrammatic primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005165 (Alternating factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ OEIS: A013916
- ^ Sloane, N. J. A. (ed.). "Sequence A006832 (Discriminants of totally real cubic fields)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A027187 (Number of partitions of n into an even number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059377 (Jordan function J_4(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A036057 (Friedman numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) = number of partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000096 (a(n) = n*(n+3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000031 (Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A101268 (Number of compositions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051868 (16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A074501 (a(n) = 1^n + 2^n + 5^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002464 (Hertzsprung's problem: ways to arrange n non-attacking kings on an n X n board, with 1 in each row and column. Also number of permutations of length n without rising or falling successions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057468 (Numbers k such that 3^k - 2^k is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001105 (a(n) = 2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (a(n) = n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A160160 (Toothpick sequence in the three-dimensional grid)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002379 (a(n) = floor(3^n / 2^n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A027480 (a(n) = n*(n+1)*(n+2)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A108917 (Number of knapsack partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A316983 (Number of non-isomorphic self-dual multiset partitions of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron with side n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A003001 (Smallest number of multiplicative persistence n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A000975 (Lichtenberg sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A000070 (a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A050535 (Number of multigraphs on infinite set of nodes with n edges)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A033553 (3-Knödel numbers or D-numbers: numbers n > 3 such that n divides k^(n-2)-k for all k with gcd(k, n) = 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A030984 (2-automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-09-01.
- ^ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000123 (Number of binary partitions: number of partitions of 2n into powers of 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A045943 (Triangular matchstick numbers: a(n) = 3*n*(n+1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A049363 (a(1) = 1; for n > 1, smallest digitally balanced number in base n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A076185 (Numbers n such that n!! + 2 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A006851 (Trails of length n on honeycomb lattice)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-18.
- ^ "Colorado is a rectangle? Think again". 23 January 2023.
- ^ Sloane, N. J. A. (ed.). "Sequence A045636 (Numbers of the form p^2 + q^2, with p and q primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.