A332040 Number of integers whose exponential divisors sum to n.

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

Offset: 1

Author

Amiram Eldar, Feb 05 2020

Keywords

• nonn

Examples

			a(6) = 2 since there are 2 solutions to esigma(x) = 6 (esigma is A051377): 4 and 6.
		

Links

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

Crossrefs

Cf. A054973, A051377, A063974, A332036, A332038.

Programs

Mathematica

f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; m = 100; v = Table[0, {m}]; Do[e = esigma[k]; If[e <= m, v[[e]]++], {k, 1, m}]; v