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

Author

Henry Bottomley, Dec 06 2003

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A011371, A054861.

Programs

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 *)

PARI

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

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