cp's OEIS Frontend

A321665 Number of strict integer partitions of n containing no 1's or prime powers.

%I A321665 #30 Dec 22 2020 10:04:52
%S A321665 1,0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,1,0,2,0,2,2,2,0,3,1,3,2,4,1,5,2,5,4,
%T A321665 6,4,9,3,8,7,10,6,13,7,13,12,16,10,20,13,22,19,24,18,32,23,34,30,37,
%U A321665 30,49,37,50,47,58,51,73,58,77,74,89,80,108,91,116
%N A321665 Number of strict integer partitions of n containing no 1's or prime powers.
%H A321665 Vaclav Kotesovec, <a href="/A321665/b321665.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..500 from Fausto A. C. Cariboni)
%F A321665 G.f.: Product_{k>=2, k not a prime power} 1 + x^k. - _Joerg Arndt_, Dec 22 2020
%e A321665 The a(36) = 9 strict integer partitions:
%e A321665   (36)
%e A321665   (30,6)
%e A321665   (21,15)
%e A321665   (22,14)
%e A321665   (24,12)
%e A321665   (26,10)
%e A321665   (18,12,6)
%e A321665   (20,10,6)
%e A321665   (14,12,10)
%t A321665 nn=100;
%t A321665 ser=Product[If[PrimePowerQ[n],1,1+x^n],{n,2,nn}];
%t A321665 CoefficientList[Series[ser,{x,0,nn}],x]
%Y A321665 Cf. A000607, A000961, A001597, A002095, A023893, A023894, A096258, A246655, A321346, A321347, A321378, A322452, A322454.
%K A321665 nonn
%O A321665 0,19
%A A321665 _Gus Wiseman_, Dec 11 2018