A090620 Highest power of 13 dividing n!.

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

Offset

0,27

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from T. D. Noe)

Formula

a(n) = A090622(n, 13) = A090623(n, 13) = [n/13]+[n/169]+[n/2197]+...

a(n) = n/12 + O(log n). - Charles R Greathouse IV, Aug 06 2012

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      a(n-1)+padic[ordp](n, 13))
    end:
seq(a(n), n=0..120);  # Alois P. Heinz, Jun 20 2020

Mathematica

IntegerExponent[Range[0, 110]!, 13] (* Harvey P. Dale, Aug 22 2011 *)
FoldList[Plus, 0, IntegerExponent[Range[100], 13]] (* T. D. Noe, Apr 10 2012 *)

Prog

(PARI) a(n)=my(t); while(n, t+=n\=13); t \\ Charles R Greathouse IV, Aug 06 2012

Crossrefs

Cf. A011371, A054861.

Sequence in context: A211663 A000195 A135663 * A151659 A057467 A074594

Adjacent sequences: A090617 A090618 A090619 * A090621 A090622 A090623

Keyword

nonn,easy

Author

Henry Bottomley, Dec 06 2003

Status

approved