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 A112623 #14 May 25 2017 09:36:47
%S A112623 0,1,1,2,1,2,1,6,2,2,1,3,1,2,2,24,1,3,1,3,2,2,1,7,2,2,6,3,1,3,1,120,2,
%T A112623 2,2,4,1,2,2,7,1,3,1,3,3,2,1,25,2,3,2,3,1,7,2,7,2,2,1,4,1,2,3,720,2,3,
%U A112623 1,3,2,3,1,8,1,2,3,3,2,3,1,25,24,2,1,4,2,2,2,7,1,4,2,3,2,2,2,121,1,3,3,4,1
%N A112623 If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = sum_{p|n} b(p,n)!.
%H A112623 Antti Karttunen, <a href="/A112623/b112623.txt">Table of n, a(n) for n = 1..10000</a>
%e A112623 45 = 3^2 * 5^1. So a(45) = 2! + 1! = 3.
%t A112623 f[n_] := Block[{fi = Last@Transpose@FactorInteger@n}, Plus @@ (fi!)]; Array[f, 101] (* _Robert G. Wilson v_, Dec 27 2005 *)
%o A112623 (PARI) A112623(n) = { my(f = factor(n)); my(s = 0); for (k=1, #f~, s = s + f[k, 2]!; ); s; } \\ _Antti Karttunen_, May 25 2017
%Y A112623 Cf. A000142.
%K A112623 nonn
%O A112623 1,4
%A A112623 _Leroy Quet_, Dec 25 2005
%E A112623 More terms from _Robert G. Wilson v_, Dec 27 2005