OFFSET
1,1
FORMULA
G.f.: Sum_{k>=1} phi(k) * log(1 + 5*x^k) / k.
a(n) = -(1/n) * Sum_{k=1..n} (-5)^gcd(n,k).
Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A261569.
MATHEMATICA
Table[-(1/n) Sum[EulerPhi[n/d] (-5)^d, {d, Divisors[n]}], {n, 1, 25}]
nmax = 25; CoefficientList[Series[Sum[EulerPhi[k] Log[1 + 5 x^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 16 2021
STATUS
approved