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

0,25

Comments

Number of integer partitions of n using elements of A126706.

Links

Table of n, a(n) for n=0..83.

Example

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

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]

Crossrefs

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

Sequence in context: A081212 A280751 A280749 * A085491 A321013 A284258

Adjacent sequences: A321933 A321934 A321935 * A321937 A321938 A321939

Keyword

nonn

Author

Gus Wiseman, Dec 11 2018

Status

approved