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| divisor = 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
| divisor = 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
}}
}}
252 (two hundred [and] fifty-two) is the [[natural number]] following [[251 (number)|251]] and preceding [[253 (number)|253]].
'''252''' ('''two hundred [and] fifty-two''') is the [[natural number]] following [[251 (number)|251]] and preceding [[253 (number)|253]].


==In mathematics==
==In mathematics==
'''252''' is:
'''252''' is:
⚫
*the [[central binomial coefficient]] <math>\tbinom{10}{5}</math>, the largest one divisible by all coefficients in the previous line<ref>{{Cite OEIS|A000984|name=Central binomial coefficients}}</ref>
*a [[composite number]].
*a [[practical number]].<ref>{{SloanesRef|A005153|name=Practical numbers}}</ref>
*<math>\tau(3)</math>, where <math>\tau</math> is the [[Ramanujan tau function]].<ref>{{Cite OEIS|A000594|name=Ramanujan's tau function}}</ref>
⚫
*<math>\sigma_3(6)</math>, where <math>\sigma_3</math> is the [[Divisor function|function that sums the cubes of the divisors]] of its argument:<ref>{{Cite OEIS|A001158|name=sigma_3(n): sum of cubes of divisors of n}}</ref>
⚫
*a [[hexagonal pyramidal number]].<ref>{{SloanesRef|A002412|name=Hexagonal pyramidal numbers, or greengrocer's numbers}}</ref>
⚫
*the [[central binomial coefficient]] <math>\tbinom{10}{5}</math>,<ref>{{SloanesRef|A000984|name=Central binomial coefficients}}</ref>
*palindromic in bases 5 (2002<sub>5</sub>), 10 (252<sub>10</sub>), 17 (EE<sub>17</sub>), 20 (CC<sub>20</sub>), 27 (99<sub>27</sub>), 35 (77<sub>35</sub>), 41 (66<sub>41</sub>), 62 (44<sub>62</sub>) and 3 other bases.
*a [[Harshad number]] in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15 (and 60 other bases).
*<math>\tau(3)</math>, where <math>\tau</math> is the [[Ramanujan tau function]].<ref>{{SloanesRef|A000594|name=Ramanujan's tau function}}</ref>
⚫
*<math>\sigma_3(6)</math>, where <math>\sigma_3</math> is the [[Divisor function|function that sums the cubes of the divisors]] of its argument:<ref>{{SloanesRef|A001158|name=sigma_3(n): sum of cubes of divisors of n}}</ref>
:<math>1^3+2^3+3^3+6^3=(1^3+2^3)(1^3+3^3)=252.</math>
:<math>1^3+2^3+3^3+6^3=(1^3+2^3)(1^3+3^3)=252.</math>
*a [[practical number]],<ref>{{Cite OEIS|A005153|name=Practical numbers}}</ref>
*the aliquot sum of 63001.
*a [[refactorable number]],<ref>{{Cite web|url=https://oeis.org/A033950|title=Sloane's A033950 : Refactorable numbers|date=2016-04-18|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-04-18}}</ref>
*part of the 59-aliquot tree. The aliquot sequence starting at 63001 is: 63001, '''252''', 476, 532, 588, 1008, 2216, 1954, 980, 1414, 1034, 694, 350, 394, 200, 265, 59, 1, 0.
⚫
*a [[hexagonal pyramidal number]].<ref>{{Cite OEIS|A002412|name=Hexagonal pyramidal numbers, or greengrocer's numbers}}</ref>
*a member of the [[Mian–Chowla sequence|Mian-Chowla sequence]].<ref>{{Cite web|url=https://oeis.org/A005282|title=Sloane's A005282 : Mian-Chowla sequence|date=2016-04-19|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-04-19}}</ref>


There are 252 points on the surface of a [[cuboctahedron]] of radius five in the [[FCC close packing|face-centered cubic]] lattice,<ref>{{Cite OEIS|A005901|name=Number of points on surface of cuboctahedron}}</ref> 252 ways of writing the number 4 as a sum of six squares of integers,<ref>{{Cite OEIS|A000141|name=Number of ways of writing n as a sum of 6 squares}}</ref> 252 ways of choosing four squares from a 4&times;4 chessboard up to reflections and rotations,<ref>{{Cite OEIS|A019318|name=Number of inequivalent ways of choosing n squares from an n X n board, considering rotations and reflections to be the same}}</ref> and 252 ways of placing three pieces on a [[Connect Four]] board.<ref>{{Cite OEIS|A090224|name=Number of possible positions for n men on a standard 7 X 6 board of Connect-Four}}</ref>
There are:
*252 points on the surface of a [[cuboctahedron]] of radius five in the fcc lattice,<ref>{{SloanesRef|A005901|name=Number of points on surface of cuboctahedron}}</ref>
*252 ways of writing the number 4 as a sum of six squares of integers,<ref>{{SloanesRef|A000141|name=Number of ways of writing n as a sum of 6 squares}}</ref>
*252 ways of choosing four squares from a 4&times;4 chessboard up to reflections and rotations,<ref>{{SloanesRef|A019318|name=Number of inequivalent ways of choosing n squares from an n X n board, considering rotations and reflections to be the same}}</ref>
*252 ways of placing four pieces on a [[Connect Four]] board.<ref>{{SloanesRef|A090224|name=Number of possible positions for n men on a standard 7 X 6 board of Connect-Four}}</ref>


==References==
==References==

Latest revision as of 17:07, 12 December 2022

← 251 252 253 →
Cardinaltwo hundred fifty-two
Ordinal252nd
(two hundred fifty-second)
Factorization22 × 32 × 7
Divisors1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
Greek numeralΣΝΒ´
Roman numeralCCLII, cclii
Binary111111002
Ternary1001003
Senary11006
Octal3748
Duodecimal19012
HexadecimalFC16

252 (two hundred [and] fifty-two) is the natural number following 251 and preceding 253.

In mathematics

[edit]

252 is:

There are 252 points on the surface of a cuboctahedron of radius five in the face-centered cubic lattice,[8] 252 ways of writing the number 4 as a sum of six squares of integers,[9] 252 ways of choosing four squares from a 4×4 chessboard up to reflections and rotations,[10] and 252 ways of placing three pieces on a Connect Four board.[11]

References

[edit]
  1. ^ Sloane, N. J. A. (ed.). "Sequence A000984 (Central binomial coefficients)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A000594 (Ramanujan's tau function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A001158 (sigma_3(n): sum of cubes of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A005153 (Practical numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ "Sloane's A033950 : Refactorable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A002412 (Hexagonal pyramidal numbers, or greengrocer's numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-19. Retrieved 2016-04-19.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A005901 (Number of points on surface of cuboctahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A000141 (Number of ways of writing n as a sum of 6 squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A019318 (Number of inequivalent ways of choosing n squares from an n X n board, considering rotations and reflections to be the same)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A090224 (Number of possible positions for n men on a standard 7 X 6 board of Connect-Four)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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