A331750 a(n) = A048675(sigma(n)).

0, 2, 2, 8, 3, 4, 3, 6, 32, 5, 4, 10, 9, 5, 5, 1024, 5, 34, 6, 11, 5, 6, 5, 8, 1024, 11, 7, 11, 7, 7, 5, 12, 6, 7, 6, 40, 129, 8, 11, 9, 11, 7, 18, 12, 35, 7, 6, 1026, 130, 1026, 7, 17, 7, 9, 7, 9, 8, 9, 8, 13, 1025, 7, 35, 1073741824, 12, 8, 66, 13, 7, 8, 7, 38, 2049, 131, 1026, 14, 7, 13, 8, 1027, 32, 13, 12, 13, 8, 20, 9

Offset: 1

Author

Antti Karttunen, Feb 05 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A048675, A324573, A331751.

Programs

Mathematica

{0}~Join~Array[Total@ Map[#[[-1]]*2^(PrimePi[#[[1]]] - 1) &, FactorInteger@ DivisorSigma[1, #]] &, 86, 2] (* Michael De Vlieger, Feb 08 2020, after Jean-François Alcover at A048675 *)

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A331750(n) = A048675(sigma(n));

Formula

a(n) = A048675(A000203(n)).

Additive with a(p^e) = A048675(sigma(p^e)) = A048675(1 + p + p^2 + ... + p^e).