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252
252 (two hundred [and] fifty-two) is the natural number following 251 and preceding 253.
252 is the central binomial coefficient \( \tbinom{10}{5} \),[1] and is \( \tau(3) \), where \( \tau \) is the Ramanujan tau function.[2] 252 is also \( \sigma_3(6) \), where \( \sigma_3 \) is the function that sums the cubes of the divisors of its argument:[3]
\( 1^3+2^3+3^3+6^3=(1^3+2^3)(1^3+3^3)=252. \)
It is a practical number,[4] and a hexagonal pyramidal number.[5] There are 252 points on the surface of a cuboctahedron of radius five in the fcc lattice,[6] 252 ways of writing the number 4 as a sum of six squares of integers,[7] 252 ways of choosing four squares from a 4×4 chessboard up to reflections and rotations,[8] and 252 ways of placing four pieces on a Connect Four board.[9]
| Cardinal | two hundred fifty-two |
|---|---|
| Ordinal | 252nd (two hundred and 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 |
| Roman numeral | CCLII |
| Binary | 111111002 |
| Ternary | 1001003 |
| Quaternary | 33304 |
| Quinary | 20025 |
| Senary | 11006 |
| Octal | 3748 |
| Duodecimal | 19012 |
| Hexadecimal | FC16 |
| Vigesimal | CC20 |
| Base 36 | 7036 |
References
"Sloane's A000984 : Central binomial coefficients", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
"Sloane's A000594 : Ramanujan's tau function", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
"Sloane's A001158 : sigma_3(n): sum of cubes of divisors of n", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
"Sloane's A005153 : Practical numbers", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
"Sloane's A002412 : Hexagonal pyramidal numbers, or greengrocer's numbers", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
"Sloane's A005901 : Number of points on surface of cuboctahedron", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
"Sloane's A000141 : Number of ways of writing n as a sum of 6 squares", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
"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.
"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.
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