A304791 Expansion of Product_{k>=1} (1 - prime(k)*x^k).

1, -2, -3, 1, 3, 18, 0, 35, -27, -85, -91, -109, -366, 118, 942, -957, 2791, 2091, 4855, -1157, -6903, 3341, 3162, -37034, -46480, -89890, 581, 131275, -296935, 167543, 108671, 801491, 616017, 2441581, -307733, -1864550, 4495872, 1158228, -2589768, -767646, -21062537

Offset: 0

Author

Ilya Gutkovskiy, May 18 2018

Keywords

• sign

Comments

Convolution inverse of A145519.

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A000040, A007441, A145519, A147655, A298159.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 - Prime[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[-Sum[d Prime[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 40}]

Formula

G.f.: Product_{k>=1} (1 - A000040(k)*x^k).