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

1,6

Links

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

Example

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

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

Crossrefs

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

Sequence in context: A258453 A025874 A256012 * A263251 A318370 A339742

Adjacent sequences: A332037 A332038 A332039 * A332041 A332042 A332043

Keyword

nonn

Author

Amiram Eldar, Feb 05 2020

Status

approved