%I #24 Jan 11 2021 10:11:16

%S 1,0,-1,-1,1,0,0,-1,1,0,1,-2,1,-1,2,-2,2,-3,3,-3,4,-4,5,-6,6,-6,8,-9,

%T 9,-11,12,-13,14,-16,19,-19,21,-25,26,-28,32,-36,38,-41,46,-50,55,-60,

%U 65,-70,77,-85,91,-99,108,-116,126,-138,149,-160,174,-188,202,-219,237,-255,274,-296

%N Expansion of Product_{k > 0} 1/(1 + x^prime(k)).

%H Seiichi Manyama, <a href="/A048165/b048165.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A184198(n) - A184199(n). - _Vaclav Kotesovec_, Jan 11 2021

%t nn=20;

%t ser=Product[1/(1+x^p),{p,Select[Range[nn],PrimeQ]}];

%t Table[SeriesCoefficient[ser,{x,0,n}],{n,nn}] (* _Gus Wiseman_, Jun 06 2018 *)

%Y Cf. A000005, A000040, A000586, A000607, A001221, A008683, A083399, A088705, A280954, A305614.

%K sign

%O 0,12

%A _N. J. A. Sloane_