A304791 - OEIS

%I #4 May 18 2018 19:49:00

%S 1,-2,-3,1,3,18,0,35,-27,-85,-91,-109,-366,118,942,-957,2791,2091,

%T 4855,-1157,-6903,3341,3162,-37034,-46480,-89890,581,131275,-296935,

%U 167543,108671,801491,616017,2441581,-307733,-1864550,4495872,1158228,-2589768,-767646,-21062537

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

%C Convolution inverse of A145519.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

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

%t nmax = 40; CoefficientList[Series[Product[(1 - Prime[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%t 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}]

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

%K sign

%O 0,2

%A _Ilya Gutkovskiy_, May 18 2018