# 252 (number)

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

 ← 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
Binary111111002
Ternary1001003
Octal3748
Duodecimal19012

## In mathematics

252 is:

• the central binomial coefficient ${\displaystyle {\tbinom {10}{5}}}$ , the largest one divisible by all coefficients in the previous line[1]
• a Harshad number in base 10.
• ${\displaystyle \tau (3)}$ , 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]
${\displaystyle 1^{3}+2^{3}+3^{3}+6^{3}=(1^{3}+2^{3})(1^{3}+3^{3})=252.}$

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.). "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. ^
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. ^
11. ^