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

1,12

Links

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

Example

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

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

Crossrefs

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

Sequence in context: A333330 A290825 A204688 * A101672 A083731 A216266

Adjacent sequences: A332035 A332036 A332037 * A332039 A332040 A332041

Keyword

nonn

Author

Amiram Eldar, Feb 05 2020

Status

approved