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

0,23

Links

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

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]

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 *)

Prog

(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

Crossrefs

Cf. A011371, A054861, A054899.

Sequence in context: A344420 A206244 A206245 * A125891 A153675 A111895

Adjacent sequences: A064455 A064456 A064457 * A064459 A064460 A064461

Keyword

easy,nonn

Author

Robert G. Wilson v, Oct 03 2001

Status

approved