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Number of integer partitions of n containing no 1's, prime powers, or squarefree numbers.
0

%I #28 Dec 12 2018 14:21:41

%S 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 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 0,14,2,6,0,22,1,10,3,20,1,15,0,26,5,12,2

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

%C Number of integer partitions of n using elements of A126706.

%e The a(56) = 7 partitions:

%e (56)

%e (28,28)

%e (36,20)

%e (44,12)

%e (20,18,18)

%e (24,20,12)

%e (20,12,12,12)

%t nn=100;

%t ser=Product[If[n==1||PrimePowerQ[n]||SquareFreeQ[n],1,1/(1-x^n)],{n,nn}];

%t CoefficientList[Series[ser,{x,0,nn}],x]

%Y Cf. A000607, A000961, A002095, A005117, A023893, A023894, A078135, A114374, A126706, A246655, A321346, A321347, A321378, A321665.

%K nonn

%O 0,25

%A _Gus Wiseman_, Dec 11 2018