A343465 a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-3)^d.

3, -3, 11, -21, 51, -119, 315, -831, 2195, -5883, 16107, -44357, 122643, -341487, 956635, -2690841, 7596483, -21522347, 61171659, -174342165, 498112275, -1426403751, 4093181691, -11767920107, 33891544419, -97764009003, 282429537947, -817028472645, 2366564736723, -6863037262207

Offset: 1

Author

Ilya Gutkovskiy, Apr 16 2021

Keywords

• sign

Crossrefs

Cf. A000010, A001867, A032308, A038064, A074763, A261582, A343466, A343467.

Programs

Mathematica

Table[-(1/n) Sum[EulerPhi[n/d] (-3)^d, {d, Divisors[n]}], {n, 1, 30}]
nmax = 30; CoefficientList[Series[Sum[EulerPhi[k] Log[1 + 3 x^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{k>=1} phi(k) * log(1 + 3*x^k) / k.

a(n) = -(1/n) * Sum_{k=1..n} (-3)^gcd(n,k).

Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A032308.

Product_{n>=1} (1 - x^n)^a(n) = g.f. for A261582.