A060067 Largest power of n which divides n!.

1, 2, 3, 4, 5, 36, 7, 64, 81, 100, 11, 248832, 13, 196, 3375, 4096, 17, 104976, 19, 160000, 9261, 484, 23, 4586471424, 15625, 676, 531441, 614656, 29, 21870000000, 31, 1073741824, 35937, 1156, 52521875, 2821109907456, 37, 1444, 59319

Offset

1,2

Links

Table of n, a(n) for n=1..39.

Formula

a(n) = n^A011776(n) = A000142(n)/A060068(n).

Example

a(12) = 12^5 = 248832 since 12! = 479001600 = 2^10*3^5*5^2*7*11 and 12 = 2^2*3.

Mathematica

Join[{1}, Table[n^IntegerExponent[n!, n], {n, 2, 40}]] (* Harvey P. Dale, May 06 2018 *)

Prog

(PARI) a(n) = if (n==1, 1, n^valuation(n!, n)); \\ Michel Marcus, Mar 23 2020

Crossrefs

Cf. A011776, A000142, A060068.

Sequence in context: A306329 A274029 A056925 * A043310 A171578 A044907

Adjacent sequences: A060064 A060065 A060066 * A060068 A060069 A060070

Keyword

nonn

Author

Henry Bottomley, Feb 19 2001

Status

approved