252 (number): Difference between revisions
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:<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> |
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It is a [[practical number]],<ref>{{SloanesRef|A005153|name=Practical numbers}}</ref> and a [[hexagonal pyramidal number]].<ref>{{SloanesRef|A002412|name=Hexagonal pyramidal numbers, or greengrocer's numbers}}</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 4×4 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> and 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> |
It is a [[practical number]],<ref>{{SloanesRef|A005153|name=Practical numbers}}</ref> a [[refactorable number]],<ref>{{Cite web|url=https://oeis.org/A033950|title=Sloane's A033950 : Refactorable numbers|last=|first=|date=2016-04-18|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-04-18}}</ref> and a [[hexagonal pyramidal number]].<ref>{{SloanesRef|A002412|name=Hexagonal pyramidal numbers, or greengrocer's numbers}}</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 4×4 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> and 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> |
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==References== |
==References== |
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Revision as of 11:27, 18 April 2016
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| Cardinal | two hundred fifty-two | |||
| Ordinal | 252nd (two hundred fifty-second) | |||
| Factorization | 22 × 32 × 7 | |||
| Divisors | 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252 | |||
| Greek numeral | ΣΝΒ´ | |||
| Roman numeral | CCLII, cclii | |||
| Binary | 111111002 | |||
| Ternary | 1001003 | |||
| Senary | 11006 | |||
| Octal | 3748 | |||
| Duodecimal | 19012 | |||
| Hexadecimal | FC16 | |||
252 (two hundred [and] fifty-two) is the natural number following 251 and preceding 253.
252 is the central binomial coefficient ,[1] and is , where is the Ramanujan tau function.[2] 252 is also , where is the function that sums the cubes of the divisors of its argument:[3]
It is a practical number,[4] a refactorable number,[5] and a hexagonal pyramidal number.[6] There are 252 points on the surface of a cuboctahedron of radius five in the fcc lattice,[7] 252 ways of writing the number 4 as a sum of six squares of integers,[8] 252 ways of choosing four squares from a 4×4 chessboard up to reflections and rotations,[9] and 252 ways of placing four pieces on a Connect Four board.[10]
References
- ^ Sloane, N. J. A. (ed.). "Sequence A000984 (Central binomial coefficients)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000594 (Ramanujan's tau function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A005153 (Practical numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A033950 : Refactorable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
- ^ Sloane, N. J. A. (ed.). "Sequence A002412 (Hexagonal pyramidal numbers, or greengrocer's numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005901 (Number of points on surface of cuboctahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.
- ^ 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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