252 (number)

← 251 252 253 →
← 250 251 252 253 254 255 256 257 258 259 → List of numbers Integers ← 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
Greek numeral	ΣΝΒ´
Roman numeral	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.

In mathematics

252 is:

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

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

• a practical number, ^[4]
• a refactorable number, ^[5]
• a hexagonal pyramidal number. ^[6]
• a member of the Mian-Chowla sequence. ^[7]

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

1. Sloane, N. J. A. (ed.). "SequenceA000984(Central binomial coefficients)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA000594(Ramanujan's tau function)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA001158(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.). "SequenceA005153(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.). "SequenceA002412(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.). "SequenceA005901(Number of points on surface of cuboctahedron)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
9. Sloane, N. J. A. (ed.). "SequenceA000141(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.). "SequenceA019318(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.). "SequenceA090224(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.