252 (number)

← 251 252 253 →
← 200 210 220 230 240 250 260 270 280 290 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	two hundred fifty-two
Ordinal	252nd (two hundred and fifty-second)
Factorization	2^2× 3^2× 7
Divisors	1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
Roman numeral	CCLII
Binary	111111002
Ternary	1001003
Quaternary	33304
Quinary	20025
Senary	11006
Octal	3748
Duodecimal	19012
Hexadecimal	FC16
Vigesimal	CC20
Base 36	7036

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

In mathematics

252 is:

• the central binomial coefficient ${\tbinom {10}{5}}$, the largest one divisible by all coefficients in the previous line^[1]
• a Harshad number in base 10.
• $\tau (3)$, where $\tau$ is the Ramanujan tau function.^[2]
• $\sigma _{3}(6)$, where $\sigma_3$ is the function that sums the cubes of the divisors of its argument:^[3]

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

• 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 fcc 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 four pieces on a Connect Four board.^[11]

References

1. "Sloane's A000984 : Central binomial coefficients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. "Sloane's A000594 : Ramanujan's tau function". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. "Sloane's A001158 : sigma_3(n): sum of cubes of divisors of n". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. "Sloane's 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's 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's A005901 : Number of points on surface of cuboctahedron". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
9. "Sloane's A000141 : Number of ways of writing n as a sum of 6 squares". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
10. "Sloane's 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's 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.