OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} k^(tau(k) - 1) * x^k/(1 - x^k).
If p is prime, a(p) = 1 + p.
MATHEMATICA
a[n_] := DivisorSum[n, #^(DivisorSigma[0, #] - 1) &]; Array[a, 40] (* Amiram Eldar, Oct 14 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, d^(numdiv(d)-1));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k^(numdiv(k)-1)*x^k/(1-x^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 14 2021
STATUS
approved