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===650s===
===650s===
* 650 = 2 × 5<sup>2</sup> × 13, [[primitive abundant number]],<ref>{{Cite web|url=https://oeis.org/A071395|title=Sloane's A071395 : Primitive abundant numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[square pyramidal number]],<ref>{{Cite web|url=https://oeis.org/A000330|title=Sloane's A000330 : Square pyramidal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</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]]
* 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]]
* 651 = 3 × 7 × 31, sphenic number, [[pentagonal number]],<ref>{{Cite web|url=https://oeis.org/A000326|title=Sloane's A000326 : Pentagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[nonagonal number]]<ref>{{Cite web|url=https://oeis.org/A001106|title=Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
* 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>
* 652 = 2<sup>2</sup> × 163, maximal number of regions by drawing 26 circles<ref>{{cite OEIS|1=A014206|2=a(n) = n^2 + n + 2|access-date=2022-05-31}}</ref>
* 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>
* 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|access-date=2022-05-31}}</ref>
* 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>.<ref>{{cite OEIS|1=A002379|2=a(n) = floor(3^n / 2^n)|access-date=2022-05-31}}</ref> In [[Judaism]], 656 is the number of times that [[Jerusalem]] is mentioned in the [[Hebrew Bible]] or [[Old Testament]].
* 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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**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.<ref name=":7" />
**Sparsely totient number.<ref name=":7" />
**Sum of 11th row when writing the natural numbers as a triangle.<ref>{{cite OEIS|1=A027480|2=a(n) = n*(n+1)*(n+2)/2|access-date=2022-05-31}}</ref>
**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
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**[[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 web|url=https://oeis.org/A005282|title=Sloane's A005282 : Mian-Chowla sequence|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
* 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|access-date=2022-05-31}}</ref>
* 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.
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===670s===
===670s===
* 670 = 2 × 5 × 67, sphenic number, [[octahedral number]],<ref>{{Cite web|url=https://oeis.org/A005900|title=Sloane's A005900 : Octahedral numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[nontotient]]
* 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&nbsp;''n''&nbsp;=&nbsp;11.
* 671 = 11 × 61. This number is the [[magic constant]] of ''n''×''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for&nbsp;''n''&nbsp;=&nbsp;11.
* 672 = 2<sup>5</sup> × 3 × 7, [[harmonic divisor number]],<ref>{{Cite web|url=https://oeis.org/A001599|title=Sloane's A001599 : Harmonic or Ore numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> Zuckerman number, [[oeis:A111592|admirable number]]
* 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, 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|access-date=2022-05-31}}</ref>
* 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 web|url=https://oeis.org/A000292|title=Sloane's A000292 : Tetrahedral numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref> [[nontotient]]
* 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].<ref>{{cite OEIS|A000975|Lichtenberg sequence|access-date=2022-05-31}}</ref>
* 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 web|url=https://oeis.org/A000979|title=Sloane's A000979 : Wagstaff primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</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 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|1=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>
* 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 web|url=https://oeis.org/A001844|title=Sloane's A001844 : Centered square numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</ref>
* 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|1=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>
* 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 web|url=https://oeis.org/A000787|title=Sloane's A000787 : Strobogrammatic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-11}}</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 OEIS|A000787|Strobogrammatic numbers}}</ref>


===690s===
===690s===
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** 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|1=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]]''.
* [[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]], 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>
* 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>

Revision as of 19:26, 14 March 2024

For the years 600, see 600s BC (decade), 600s, and 600.
"611 (number)" redirects here. For the phone number, see 6-1-1. For other topics, see 611 (disambiguation).
← 599 600 601 →
Cardinalsix hundred
Ordinal600th
(six hundredth)
Factorization23 × 3 × 52
Divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
Greek numeralΧ´
Roman numeralDC
Binary10010110002
Ternary2110203
Senary24406
Octal11308
Duodecimal42012
Hexadecimal25816

600 (six hundred) is the natural number following 599 and preceding 601.

Mathematical properties

Six hundred is a composite number, an abundant number, a pronic number[1] and a Harshad number.

Credit and cars

  • 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

600s

610s

620s

630s

640s

650s

660s

670s

680s

  • 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

  • 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 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]

References

  1. ^ 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.
  2. ^ a b Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ a b Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ a b Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ 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.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ a b Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ 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.
  11. ^ 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.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A007597 (Strobogrammatic primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A005165 (Alternating factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^ OEIS: A013916
  15. ^ Sloane, N. J. A. (ed.). "Sequence A006832 (Discriminants of totally real cubic fields)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^ 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.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A059377 (Jordan function J_4(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ 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.
  19. ^ a b Sloane, N. J. A. (ed.). "Sequence A036057 (Friedman numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) = number of partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ 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.
  22. ^ a b Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  23. ^ a b Sloane, N. J. A. (ed.). "Sequence A000096 (a(n) = n*(n+3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. ^ a b c Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  26. ^ 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.
  27. ^ a b Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  28. ^ Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  29. ^ 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.
  30. ^ 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.
  31. ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  33. ^ 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.
  34. ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  36. ^ a b Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  37. ^ 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.
  38. ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  39. ^ Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  40. ^ 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.
  41. ^ 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.
  42. ^ Sloane, N. J. A. (ed.). "Sequence A001105 (a(n) = 2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  43. ^ Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  44. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  45. ^ Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  46. ^ Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  47. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (a(n) = n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  48. ^ Sloane, N. J. A. (ed.). "Sequence A160160 (Toothpick sequence in the three-dimensional grid)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  49. ^ Sloane, N. J. A. (ed.). "Sequence A002379 (a(n) = floor(3^n / 2^n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  50. ^ Sloane, N. J. A. (ed.). "Sequence A027480 (a(n) = n*(n+1)*(n+2)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  51. ^ Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  52. ^ Sloane, N. J. A. (ed.). "Sequence A108917 (Number of knapsack partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  53. ^ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  54. ^ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  55. ^ 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.
  56. ^ 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.
  57. ^ 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.
  58. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  59. ^ Sloane, N. J. A. (ed.). "Sequence A000975 (Lichtenberg sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
  60. ^ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  61. ^ 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.
  62. ^ Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  63. ^ 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.
  64. ^ 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.
  65. ^ Sloane, N. J. A. (ed.). "Sequence A030984 (2-automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-09-01.
  66. ^ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  67. ^ 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.
  68. ^ 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.
  69. ^ 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.
  70. ^ 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.
  71. ^ 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.
  72. ^ "Colorado is a rectangle? Think again". 23 January 2023.
  73. ^ 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.
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