A332038 Number of integers whose infinitary divisors sum to n.

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, 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, 0, 1, 0, 5, 0, 1, 0, 0, 0, 1, 0, 3, 0, 1, 0, 2, 1, 0, 0

Offset: 1

Author

Amiram Eldar, Feb 05 2020

Keywords

• nonn

Examples

			a(12) = 2 since there are 2 solutions to isigma(x) = 12 (isigma is A049417): 6 and 11.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054973, A049417, A063974, A332036, A332040.

Programs

Mathematica

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