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A064459 a(n) = Sum_{k>=1} floor(n/12^k).

%I A064459 #19 Mar 24 2018 06:07:49
%S A064459 0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,
%T A064459 2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,
%U A064459 5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8
%N A064459 a(n) = Sum_{k>=1} floor(n/12^k).
%C A064459 Original incorrect name was: "Highest power of 12 dividing n!": that sequence is A090619.  If p is prime, Legendre's formula says the highest power of p dividing n! is Sum_{k>=1} floor(n/p^k), but of course 12 is not prime. - _Robert Israel_, Mar 23 2018
%H A064459 Harry J. Smith, <a href="/A064459/b064459.txt">Table of n, a(n) for n=0..1000</a>
%H A064459 Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre%27s_formula">Legendre's formula</a>.
%F A064459 a(n) = floor[n/12] + floor[n/144] + floor[n/1728] + floor[n/20736] + ....
%p A064459 f:= proc(n) add(floor(n/12^k), k=1..floor(log[12](n))) end proc:
%p A064459 f(0):= 0:
%p A064459 map(f, [$0..100]); # _Robert Israel_, Mar 23 2018
%t A064459 Table[t = 0; p = 12; While[s = Floor[n/p]; t = t + s; s > 0, p *= 12]; t, {n, 0, 100} ]
%t A064459 Join[{0},Accumulate[Table[If[Divisible[n,12],1,0],{n,110}]]] (* _Harvey P. Dale_, Feb 14 2016 *)
%o A064459 (PARI) { for (n=0, 1000, a=0; p=12; while (s = n\p, a+=s; p*=12); write("b064459.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 15 2009
%o A064459 (GAP) List([0..110],n->Sum([1..n],k-?Int(n/(12^k)))); # _Muniru A Asiru_, Mar 24 2018
%Y A064459 Cf. A011371, A054861, A090619.
%K A064459 easy,nonn
%O A064459 0,25
%A A064459 _Robert G. Wilson v_, Oct 03 2001
%E A064459 Corrected by _Robert Israel_, Mar 23 2018