A329098 - OEIS

%I #4 Nov 05 2019 01:02:07

%S 1,0,-1,-1,0,1,2,0,-3,-3,2,5,4,-4,-10,-5,10,16,5,-20,-27,0,41,38,-14,

%T -73,-55,46,134,63,-118,-219,-55,252,356,-11,-510,-527,198,951,734,

%U -644,-1702,-867,1579,2864,764,-3415,-4609,84,6808,6897,-2526,-12745,-9539,8383

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

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

%t nmax = 55; CoefficientList[Series[1/(1 + Sum[Boole[PrimePowerQ[k]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = -Sum[Boole[PrimePowerQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 55}]

%Y Cf. A002121, A246655, A280195.

%K sign

%O 0,7

%A _Ilya Gutkovskiy_, Nov 04 2019