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