%I #4 Nov 05 2019 01:02:01

%S 1,0,-1,-1,0,0,1,0,0,-1,1,0,1,-1,1,-1,1,-2,2,-2,2,-2,3,-4,3,-4,5,-5,6,

%T -6,7,-8,9,-9,11,-12,13,-16,15,-17,20,-22,23,-26,29,-30,35,-38,40,-45,

%U 50,-52,58,-65,69,-75,82,-89,96,-107,114,-123,135,-145,158,-170,185,-200,216,-232,251

%N Expansion of Product_{p prime, k>=1} 1 / (1 + x^(p^k)).

%C Convolution inverse of A054685.

%F G.f.: Product_{k>=1} 1 / (1 + x^A246655(k)).

%t nmax = 70; CoefficientList[Series[Product[1/(1 + Boole[PrimePowerQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%t a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d) Boole[PrimePowerQ[d]] d, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 70}]

%Y Cf. A023894, A048165, A054685, A246655, A328556.

%K sign

%O 0,18

%A _Ilya Gutkovskiy_, Nov 04 2019