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A321346 Number of integer partitions of n containing no prime powers > 1.

%I A321346 #31 Dec 27 2020 03:35:14
%S A321346 1,1,1,1,1,1,2,2,2,2,3,3,5,5,6,7,8,8,11,11,14,16,19,19,25,26,31,34,40,
%T A321346 41,52,54,63,69,81,86,105,109,126,137,160,169,201,211,242,264,303,320,
%U A321346 375,396,453,490,557,590,682,726,823,888,1002,1065,1219
%N A321346 Number of integer partitions of n containing no prime powers > 1.
%C A321346 First differs from A285798 at a(30) = 52, A285798(30) = 51.
%H A321346 Fausto A. C. Cariboni, <a href="/A321346/b321346.txt">Table of n, a(n) for n = 0..350</a>
%e A321346 The a(20) = 14 integer partitions:
%e A321346   (20)
%e A321346   (10,10)
%e A321346   (14,6)
%e A321346   (18,1,1)
%e A321346   (12,6,1,1)
%e A321346   (6,6,6,1,1)
%e A321346   (10,6,1,1,1,1)
%e A321346   (15,1,1,1,1,1)
%e A321346   (14,1,1,1,1,1,1)
%e A321346   (12,1,1,1,1,1,1,1,1)
%e A321346   (6,6,1,1,1,1,1,1,1,1)
%e A321346   (10,1,1,1,1,1,1,1,1,1,1)
%e A321346   (6,1,1,1,1,1,1,1,1,1,1,1,1,1,1)
%e A321346   (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)
%t A321346 nn=100;
%t A321346 ser=Product[If[PrimePowerQ[n],1,1/(1-x^n)],{n,nn}];
%t A321346 CoefficientList[Series[ser,{x,0,nn}],x]
%Y A321346 Cf. A000607, A000961, A001597, A002095, A023893, A023894,  A096258, A246655, A320322, A321347, A321378, A321665, A322452, A322454.
%K A321346 nonn
%O A321346 0,7
%A A321346 _Gus Wiseman_, Dec 11 2018