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

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

Offset: 0

Author

Gus Wiseman, Dec 11 2018

Keywords

• nonn

Comments

Number of integer partitions of n using elements of A126706.

Examples

			The a(56) = 7 partitions:
  (56)
  (28,28)
  (36,20)
  (44,12)
  (20,18,18)
  (24,20,12)
  (20,12,12,12)
		

Crossrefs

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

Programs

Mathematica

nn=100;
ser=Product[If[n==1||PrimePowerQ[n]||SquareFreeQ[n],1,1/(1-x^n)],{n,nn}];
CoefficientList[Series[ser,{x,0,nn}],x]