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 A113308 #13 Mar 15 2015 15:57:15
%S A113308 1,1,1,2,1,3,1,4,2,5,1,8,1,7,4,10,1,13,1,15,6,11,1,27,2,13,8,28,1,27,
%T A113308 1,36,10,17,4,62,1,19,12,59,1,47,1,66,19,23,1,118,2,31,16,91,1,78,8,
%U A113308 117,18,29,1,193,1,31,26,159,10,115,1,153,22,51,1,320,1,37,35,190,6,161,1
%N A113308 a(n) = the number of finite sequences of positive integers {b(k)} where (product b(k))* (sum b(k)) = n. Different orderings of the same integers are counted separately.
%C A113308 Sequence's terms calculated by "Max".
%F A113308 a(n)=1 if n=1 or is a prime, a(2)=2 if n is the square of a prime. - _Robert G. Wilson v_
%e A113308 6 = 1*1*1*1*1*1*(1+1+1+1+1+1) = 1*2*(1+2) = 2*1*(2+1). So a(6) = 3.
%t A113308 (* first do *) Needs["DiscreteMath`Combinatorica`"] ( then *) t = Table[1, {80}]; Do[k = 1; lmt = PartitionsP@n; p = Partitions@n; While[k < lmt, a = Plus @@ p[[k]]*Times @@ p[[k]]; If[a < 81, t[[a]] += Length@ Permutations@ p[[k]]]; k++ ], {n, 40}]; t (* _Robert G. Wilson v_, May 03 2006 *)
%Y A113308 Cf. A113309.
%K A113308 nonn
%O A113308 1,4
%A A113308 _Leroy Quet_, Oct 25 2005