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