cp's OEIS Frontend

A321378 Number of integer partitions of n containing no 1's or prime powers.

%I A321378 #32 Dec 12 2018 14:21:26
%S A321378 1,0,0,0,0,0,1,0,0,0,1,0,2,0,1,1,1,0,3,0,3,2,3,0,6,1,5,3,6,1,11,2,9,6,
%T A321378 12,5,19,4,17,11,23,9,32,10,31,22,39,17,55,21,57,37,67,33,92,44,97,65,
%U A321378 114,63,154,78,162,113,191,117,250,138,269,194,320
%N A321378 Number of integer partitions of n containing no 1's or prime powers.
%e A321378 The a(30) = 11 integer partitions:
%e A321378   (30)
%e A321378   (24,6)
%e A321378   (15,15)
%e A321378   (18,12)
%e A321378   (20,10)
%e A321378   (18,6,6)
%e A321378   (12,12,6)
%e A321378   (14,10,6)
%e A321378   (10,10,10)
%e A321378   (12,6,6,6)
%e A321378   (6,6,6,6,6)
%t A321378 nn=100;
%t A321378 ser=Product[If[PrimePowerQ[n],1,1/(1-x^n)],{n,2,nn}];
%t A321378 CoefficientList[Series[ser,{x,0,nn}],x]
%Y A321378 Cf. A000607, A000688, A000961, A002095, A023893, A023894, A096258, A246655, A320322, A321346, A321347, A321665, A322452, A322454.
%K A321378 nonn
%O A321378 0,13
%A A321378 _Gus Wiseman_, Dec 11 2018