This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090619 #20 Mar 27 2018 10:58:13
%S A090619 0,0,0,0,1,1,2,2,2,3,4,4,5,5,5,5,6,6,8,8,8,9,9,9,10,10,10,11,12,12,13,
%T A090619 13,14,15,15,15,17,17,17,17,18,18,19,19,19,20,21,21,22,22,22,23,23,23,
%U A090619 25,25,26,26,27,27,28,28,28,28,30,30,31,31,31,32,32,32,34,34,34,35,35
%N A090619 Highest power of 12 dividing n!.
%C A090619 Most sequences of the form "highest power of k dividing n!" essentially depend on one of the primes or prime powers dividing k. But in this case, the sequences with k=3 (A054861) and k=4 (A090616) are both close to n/2 and vary in which one is lower for different values of n.
%C A090619 a(2^n) = A090616(2^n) and a(3^n-1) = A090616(3^n-1) while a(2^n-1) = A054861(2^n-1) and a(3^n) = A054861(3^n). - _Robert Israel_, Mar 25 2018
%H A090619 Robert Israel, <a href="/A090619/b090619.txt">Table of n, a(n) for n = 0..10000</a>
%F A090619 a(n) =A090622(n, 12) =min(A054861(n), A090616(n)). Close to n/2, indeed for n>3: n/2-log3(n+1) <= a(n) < n/2.
%e A090619 a(6)=2 since 6!=720=12^2*5.
%p A090619 f2:= n -> n - convert(convert(n,base,2),`+`):
%p A090619 f3:= n -> (n - convert(convert(n,base,3),`+`))/2:
%p A090619 f:= n -> min(f3(n), floor(f2(n)/2)):
%p A090619 f(0):= 0:
%p A090619 map(f, [$0..100]); # _Robert Israel_, Mar 23 2018
%t A090619 Table[IntegerExponent[n!, 12], {n, 0, 100}] (* _Jean-François Alcover_, Mar 26 2018 *)
%o A090619 (PARI) a(n) = valuation(n!, 12); \\ _Michel Marcus_, Mar 24 2018
%Y A090619 Cf. A011371, A054861, A090616, A027868, A054896, A090617, A090618.
%K A090619 nonn
%O A090619 0,7
%A A090619 _Henry Bottomley_, Dec 06 2003