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252 (number)

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From Wikipedia, the free encyclopedia

Natural number

← 251

252

253 →

←250 251 252 253 254 255 256 257 258 259 →

←0 100 200 300 400 500 600 700 800 900 →

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

ΣΝΒ´

CCLII,cclii

11111100₂

100100₃

1100₆

374₈

190₁₂

FC₁₆

252 (two hundred [and] fifty-two) is thenatural number following251 and preceding253.

In mathematics

[edit]

252 is:

thecentral binomial coefficient ${\tbinom {10}{5}}$ , the largest one divisible by all coefficients in the previous line^[1]
$\tau (3)$ , where $\tau$ is theRamanujan tau function.^[2]
$\sigma _{3}(6)$ , where $\sigma _{3}$ is thefunction that sums the cubes of the divisors of its argument:^[3]

1^{3}+2^{3}+3^{3}+6^{3}=(1^{3}+2^{3})(1^{3}+3^{3})=252.

apractical number,^[4]
arefactorable number,^[5]
ahexagonal pyramidal number.^[6]
a member of theMian-Chowla sequence.^[7]

There are 252 points on the surface of acuboctahedron of radius five in theface-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 aConnect Four board.^[11]

References

[edit]

^Sloane, N. J. A. (ed.)."Sequence A000984 (Central binomial coefficients)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000594 (Ramanujan's tau function)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A001158 (sigma_3(n): sum of cubes of divisors of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A005153 (Practical numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^"Sloane's A033950 : Refactorable numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-18. Retrieved2016-04-18.
^Sloane, N. J. A. (ed.)."Sequence A002412 (Hexagonal pyramidal numbers, or greengrocer's numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^"Sloane's A005282 : Mian-Chowla sequence".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-19. Retrieved2016-04-19.
^Sloane, N. J. A. (ed.)."Sequence A005901 (Number of points on surface of cuboctahedron)".TheOn-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)".TheOn-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)".TheOn-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)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.

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