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

Author

Henry Bottomley, Feb 19 2001

Keywords

• nonn

Examples

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

Crossrefs

Cf. A011776, A000142, A060068.

Programs

Mathematica

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

PARI

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

Formula

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