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A321936 Number of integer partitions of n containing no 1's, prime powers, or squarefree numbers.

%I A321936 #28 Dec 12 2018 14:21:41
%S A321936 1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,2,0,0,0,1,0,1,0,1,0,
%T A321936 0,0,4,0,1,0,3,0,2,0,3,1,1,0,7,0,2,0,5,0,5,0,7,1,3,0,12,0,4,2,10,1,8,
%U A321936 0,14,2,6,0,22,1,10,3,20,1,15,0,26,5,12,2
%N A321936 Number of integer partitions of n containing no 1's, prime powers, or squarefree numbers.
%C A321936 Number of integer partitions of n using elements of A126706.
%e A321936 The a(56) = 7 partitions:
%e A321936   (56)
%e A321936   (28,28)
%e A321936   (36,20)
%e A321936   (44,12)
%e A321936   (20,18,18)
%e A321936   (24,20,12)
%e A321936   (20,12,12,12)
%t A321936 nn=100;
%t A321936 ser=Product[If[n==1||PrimePowerQ[n]||SquareFreeQ[n],1,1/(1-x^n)],{n,nn}];
%t A321936 CoefficientList[Series[ser,{x,0,nn}],x]
%Y A321936 Cf. A000607, A000961, A002095, A005117, A023893, A023894, A078135, A114374, A126706, A246655, A321346, A321347, A321378, A321665.
%K A321936 nonn
%O A321936 0,25
%A A321936 _Gus Wiseman_, Dec 11 2018