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%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
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