%I #9 Feb 06 2020 00:48:10
%S 1,0,1,1,1,1,0,1,0,1,0,2,0,1,1,0,1,2,0,2,0,0,0,3,0,1,0,0,0,3,0,2,0,0,
%T 0,1,0,1,0,2,0,2,0,1,0,0,0,3,0,2,1,0,0,2,0,1,0,0,0,5,0,1,0,0,0,0,0,2,
%U 0,1,0,5,0,1,0,0,0,1,0,3,0,1,0,2,1,0,0
%N Number of integers whose infinitary divisors sum to n.
%H Amiram Eldar, <a href="/A332038/b332038.txt">Table of n, a(n) for n = 1..10000</a>
%e a(12) = 2 since there are 2 solutions to isigma(x) = 12 (isigma is A049417): 6 and 11.
%t fun[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ (fun @@@ FactorInteger[n]); m = 100; v = Table[0, {m}]; Do[i = isigma[k]; If[i <= m, v[[i]]++], {k, 1, m}]; v
%Y Cf. A054973, A049417, A063974, A332036, A332040.
%K nonn
%O 1,12
%A _Amiram Eldar_, Feb 05 2020