OFFSET
1,3
FORMULA
G.f.: Sum_{k>=1} mu(k) * x^k/(1 - k * x^k)^2.
If p is prime, a(p) = p - 1.
MATHEMATICA
a[n_] := DivisorSum[n, MoebiusMu[n/#] * # * (n/#)^(#-1) &]; Array[a, 45] (* Amiram Eldar, Aug 27 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*(n/d)^(d-1));
(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, moebius(k)*x^k/(1-k*x^k)^2))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Dec 19 2022
STATUS
approved