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A329097
Expansion of Product_{p prime, k>=1} 1 / (1 + x^(p^k)).
0
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, -6, 7, -8, 9, -9, 11, -12, 13, -16, 15, -17, 20, -22, 23, -26, 29, -30, 35, -38, 40, -45, 50, -52, 58, -65, 69, -75, 82, -89, 96, -107, 114, -123, 135, -145, 158, -170, 185, -200, 216, -232, 251
OFFSET
0,18
COMMENTS
Convolution inverse of A054685.
FORMULA
G.f.: Product_{k>=1} 1 / (1 + x^A246655(k)).
MATHEMATICA
nmax = 70; CoefficientList[Series[Product[1/(1 + Boole[PrimePowerQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
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}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 04 2019
STATUS
approved