A343465 - OEIS

%I #7 Apr 16 2021 15:41:48

%S 3,-3,11,-21,51,-119,315,-831,2195,-5883,16107,-44357,122643,-341487,

%T 956635,-2690841,7596483,-21522347,61171659,-174342165,498112275,

%U -1426403751,4093181691,-11767920107,33891544419,-97764009003,282429537947,-817028472645,2366564736723,-6863037262207

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

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

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

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

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

%t Table[-(1/n) Sum[EulerPhi[n/d] (-3)^d, {d, Divisors[n]}], {n, 1, 30}]

%t nmax = 30; CoefficientList[Series[Sum[EulerPhi[k] Log[1 + 3 x^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

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

%K sign

%O 1,1

%A _Ilya Gutkovskiy_, Apr 16 2021