%I #19 Jun 20 2020 16:10:35
%S 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,
%T 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,
%U 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
%N Highest power of 13 dividing n!.
%H Alois P. Heinz, <a href="/A090620/b090620.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from T. D. Noe)
%F a(n) = A090622(n, 13) = A090623(n, 13) = [n/13]+[n/169]+[n/2197]+...
%F a(n) = n/12 + O(log n). - _Charles R Greathouse IV_, Aug 06 2012
%p a:= proc(n) option remember; `if`(n=0, 0,
%p a(n-1)+padic[ordp](n, 13))
%p end:
%p seq(a(n), n=0..120); # _Alois P. Heinz_, Jun 20 2020
%t IntegerExponent[Range[0,110]!,13] (* _Harvey P. Dale_, Aug 22 2011 *)
%t FoldList[Plus, 0, IntegerExponent[Range[100], 13]] (* _T. D. Noe_, Apr 10 2012 *)
%o (PARI) a(n)=my(t);while(n,t+=n\=13);t \\ _Charles R Greathouse IV_, Aug 06 2012
%Y Cf. A011371, A054861.
%K nonn,easy
%O 0,27
%A _Henry Bottomley_, Dec 06 2003