OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
If p is an odd prime, a(p) = 0.
G.f.: Sum_{k>=1} (-1)^(sigma(k) - 1) * x^k/(1 - x^k).
From Bernard Schott, Oct 19 2021: (Start)
If p is even prime = 2, a(2^k) = k+1 for k >= 0.
If p is odd prime, a(p^even) = 1 and a(p^odd) = 0 (compare with formulas in A347992). (End)
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^(DivisorSigma[1, #] - 1) &]; Array[a, 100] (* Amiram Eldar, Oct 08 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, (-1)^(sigma(d)-1));
(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, (-1)^(sigma(k)-1)*x^k/(1-x^k)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 08 2021
STATUS
approved