A329098 Expansion of 1 / (1 + Sum_{p prime, k>=1} x^(p^k)).

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, -73, -55, 46, 134, 63, -118, -219, -55, 252, 356, -11, -510, -527, 198, 951, 734, -644, -1702, -867, 1579, 2864, 764, -3415, -4609, 84, 6808, 6897, -2526, -12745, -9539, 8383

Offset: 0

Author

Ilya Gutkovskiy, Nov 04 2019

Keywords

• sign

Crossrefs

Cf. A002121, A246655, A280195.

Programs

Mathematica

nmax = 55; CoefficientList[Series[1/(1 + Sum[Boole[PrimePowerQ[k]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[Boole[PrimePowerQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 55}]

Formula

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