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A348127 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} x^prime(n).

%I A348127 #10 Mar 02 2022 02:51:47
%S A348127 0,1,1,-1,0,-1,1,-1,-1,-1,2,0,0,-3,0,0,3,-3,-1,-1,4,-4,-1,-5,6,2,2,
%T A348127 -17,4,4,13,-16,-7,-11,30,-14,-7,-34,42,7,16,-80,27,6,95,-117,-21,-60,
%U A348127 223,-97,-48,-265,326,53,129,-800,242,93,752,-948,-105,-499,1806,-853,-240,-2189,2750,124
%N A348127 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} x^prime(n).
%H A348127 Robert Israel, <a href="/A348127/b348127.txt">Table of n, a(n) for n = 1..2500</a>
%p A348127 N:= 20: # for a(1)..a(N)
%p A348127 P:= 1: a:= Vector(N):
%p A348127 for n from 1 to N do
%p A348127   c:= coeff(P,x,n);
%p A348127   if isprime(n) then a[n]:= 1-c  else a[n]:= -c fi;
%p A348127   P:= series(P/(1-a[n]*x^n),x,N+1);
%p A348127 od:
%p A348127 convert(a,list); # _Robert Israel_, Mar 01 2022
%Y A348127 Cf. A000040, A002121, A010051, A030010, A147557, A305871, A305882, A308298, A328777, A348128.
%K A348127 sign
%O A348127 1,11
%A A348127 _Ilya Gutkovskiy_, Oct 01 2021