A064458 Highest power of 11 dividing n!.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9

Offset: 0

Author

Robert G. Wilson v, Oct 03 2001

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A011371, A054861, A054899.

Programs

Mathematica

Table[t = 0; p = 11; While[s = Floor[n/p]; t = t + s; s > 0, p *= 11]; t, {n, 0, 100} ]
IntegerExponent[Range[0,110]!,11] (* Harvey P. Dale, Aug 07 2017 *)

PARI

{ for (n=0, 1000, a=0; p=11; while (s = n\p, a+=s; p*=11); write("b064458.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 14 2009

PARI

a(n) = valuation(n!, 11); \\ Michel Marcus, Apr 07 2016

Formula

a(n) = floor[n/11] + floor[n/121] + floor[n/1331] + floor[n/14641] + ....

a(n) = (n-A053831(n))/10. [R. J. Mathar, Oct 17 2010]