A298159 -id:A298159 - cp's OEIS frontend

A298160 G.f.: Product_{k>=1} 1/(1+prime(k)*x^prime(k)).

1, 0, -2, -3, 4, 1, 1, -9, 13, -9, 20, -38, 76, -75, 65, -323, 378, -197, 805, -1394, 1635, -2513, 3175, -5442, 11135, -12570, 12526, -33357, 51563, -46460, 93551, -155750, 186650, -313241, 421641, -620393, 1131820, -1321220, 1663951, -3559915, 5011036, -5207116

Offset: 0

Seiichi Manyama, Jan 14 2018

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Seiichi Manyama, Table of n, a(n) for n = 0..6278

Cf. A002099, A048165, A298159.

CoefficientList[Series[Product[1/(1+Prime[k]x^Prime[k]),{k,50}],{x,0,50}],x] (* Harvey P. Dale, Mar 24 2020 *)

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

Original entry on oeis.org

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

Ilya Gutkovskiy, May 18 2018

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Convolution inverse of A145519.

Index entries for sequences related to partitions

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

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}]

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

cp's OEIS Frontend

A298160 G.f.: Product_{k>=1} 1/(1+prime(k)*x^prime(k)).

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