A343466 a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-4)^d.

4, -6, 24, -66, 208, -676, 2344, -8226, 29144, -104760, 381304, -1398476, 5162224, -19172796, 71582944, -268439586, 1010580544, -3817734596, 14467258264, -54975633768, 209430787824, -799644629556, 3059510616424, -11728124734476, 45035996273872, -173215367702376, 667199944815064

Offset: 1

Author

Ilya Gutkovskiy, Apr 16 2021

Keywords

• sign

Crossrefs

Cf. A000010, A001868, A038065, A074763, A261568, A343465, A343467.

Programs

Mathematica

Table[-(1/n) Sum[EulerPhi[n/d] (-4)^d, {d, Divisors[n]}], {n, 1, 27}]
nmax = 27; CoefficientList[Series[Sum[EulerPhi[k] Log[1 + 4 x^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{k>=1} phi(k) * log(1 + 4*x^k) / k.

a(n) = -(1/n) * Sum_{k=1..n} (-4)^gcd(n,k).

Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A261568.