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== In mathematics ==
== In mathematics ==
* Although composite, 145 is a [[Fermat pseudoprime]] to sixteen bases with b < 145. In four of those bases, it is a [[strong pseudoprime]]: 1, 12, 17, and 144.
* Although composite, 145 is a [[Fermat pseudoprime]] in [[16 (number)|sixteen]] bases with b < 145. In four of those bases, it is a [[strong pseudoprime]]: 1, 12, 17, and 144.
* Given 145, the [[Mertens function]] returns [[0 (number)|0]].<ref>{{Cite web|url=https://oeis.org/A028442|title=Sloane's A028442 : Numbers n such that Mertens' function is zero|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref>
* the [[Mertens function]] returns [[0 (number)|0]].<ref>{{Cite web|url=https://oeis.org/A028442|title=Sloane's A028442 : Numbers n such that Mertens' function is zero|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref>
* 145 is a [[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=2016-05-28}}</ref> and a [[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=2016-05-28}}</ref>
* 145 is a [[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=2016-05-28}}</ref> and a [[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=2016-05-28}}</ref>
* <math>145 = 12^2 + 1^2 = 8^2 + 9^2</math>. 145 is the fourth number that is the sum of two different pairs of [[square (algebra)|squares]]. Also, 145 is the result of 3<sup>4</sup> + 4<sup>3</sup>, making it a [[Leyland number]].
* <math>145 = 12^2 + 1^2 = 8^2 + 9^2</math>. 145 is the fourth number that is the sum of two different pairs of [[square (algebra)|squares]]. Also, 145 is the result of 3<sup>4</sup> + 4<sup>3</sup>, making it a [[Leyland number]].
* <math>145 = 1! + 4! + 5!</math>, making it a [[factorion]].<ref name=":0">{{Cite web|url=https://oeis.org/A014080|title=Sloane's A014080 : Factorions|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref> The only other numbers that have the property that they are the sum of the [[factorial]]s of their digits are [[1 (number)|1]], [[2 (number)|2]] and 40585.<ref name=":0" />
* <math>145 = 1! + 4! + 5!</math>, making it a [[factorion]].<ref name=":0">{{Cite web|url=https://oeis.org/A014080|title=Sloane's A014080 : Factorions|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref> The only other numbers that have this property are [[1 (number)|1]], [[2 (number)|2]] and [[40,000|40585]].<ref name=":0" />
* <math>145=5^2+5!=11^2+4!=12^2+1!</math>, making 145 the smallest number that can be written as the sum of a perfect square and a factorial in more than 2 distinct ways. The next number with this property is 46249.<ref>{{Cite web |title=A359013 - OEIS |url=https://oeis.org/A359013 |access-date=2022-12-11 |website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundatio}}</ref>
* <math>145=5^2+5!=11^2+4!=12^2+1!</math>, making 145 the smallest number that can be written as the sum of a [[Square number|square]] number and a factorial in 3 ways. The next number with this property is [[40,000|46249]].<ref>{{Cite web |title=A359013 - OEIS |url=https://oeis.org/A359013 |access-date=2022-12-11 |website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation}}</ref>


==In the military==
==In the military==

Latest revision as of 20:17, 5 March 2024

← 144 145 146 →
Cardinalone hundred forty-five
Ordinal145th
(one hundred forty-fifth)
Factorization5 × 29
Divisors1, 5, 29, 145
Greek numeralΡΜΕ´
Roman numeralCXLV
Binary100100012
Ternary121013
Senary4016
Octal2218
Duodecimal10112
Hexadecimal9116

145 (one hundred [and] forty-five) is the natural number following 144 and preceding 146.

In mathematics

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  • Although composite, 145 is a Fermat pseudoprime in sixteen bases with b < 145. In four of those bases, it is a strong pseudoprime: 1, 12, 17, and 144.
  • the Mertens function returns 0.[1]
  • 145 is a pentagonal number[2] and a centered square number.[3]
  • . 145 is the fourth number that is the sum of two different pairs of squares. Also, 145 is the result of 34 + 43, making it a Leyland number.
  • , making it a factorion.[4] The only other numbers that have this property are 1, 2 and 40585.[4]
  • , making 145 the smallest number that can be written as the sum of a square number and a factorial in 3 ways. The next number with this property is 46249.[5]

In the military

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In sports

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In transportation

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In other fields

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145 is also:

See also

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References

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  1. ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  2. ^ "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  3. ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  4. ^ a b "Sloane's A014080 : Factorions". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  5. ^ "A359013 - OEIS". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-11.
  6. ^ "1938 Delahaye 145 le mans Slot Car 1/32". www.tertrerouge-racingcars.com. Archived from the original on 16 September 2008. Retrieved 14 January 2022.
  7. ^ "Ferry Schedules & Maps - Ferry | Golden Gate".
  8. ^ "Route 145". London Bus Routes.
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