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%I #8 Feb 11 2021 11:19:52
%S 1,0,1,1,2,3,6,8,15,23,40,63,108,172,290,471,782,1280,2119,3474,5741,
%T 9432,15557,25590,42180,69413,114371,188276,310136,510637,841045,
%U 1384883,2280831,3755862,6185457,10185941,16774695,27624215,45492412,74916559,123374127,203172520,334587577
%N Expansion of 1/(1 - Sum_{k>=1} x^prime(k)/(1 - x^prime(k))).
%C Invert transform of A001221.
%H Alois P. Heinz, <a href="/A300671/b300671.txt">Table of n, a(n) for n = 0..2000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F G.f.: 1/(1 - Sum_{k>=2} A001221(k)*x^k).
%p a:= proc(n) option remember; `if`(n=0, 1,
%p add(a(n-i)*nops(ifactors(i)[2]), i=1..n))
%p end:
%p seq(a(n), n=0..42); # _Alois P. Heinz_, Feb 11 2021
%t nmax = 42; CoefficientList[Series[1/(1 - Sum[x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}]), {x, 0, nmax}], x]
%t nmax = 42; CoefficientList[Series[1/(1 - Sum[PrimeNu[k] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = Sum[PrimeNu[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 42}]
%Y Cf. A001221, A013939, A112965, A129921, A180305, A293548, A300672.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Mar 11 2018
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