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

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, 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, 30, 49, 37, 50, 47, 58, 51, 73, 58, 77, 74, 89, 80, 108, 91, 116

Offset: 0

Author

Gus Wiseman, Dec 11 2018

Keywords

• nonn

Examples

			The a(36) = 9 strict integer partitions:
  (36)
  (30,6)
  (21,15)
  (22,14)
  (24,12)
  (26,10)
  (18,12,6)
  (20,10,6)
  (14,12,10)
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..500 from Fausto A. C. Cariboni)

Crossrefs

Cf. A000607, A000961, A001597, A002095, A023893, A023894, A096258, A246655, A321346, A321347, A321378, A322452, A322454.

Programs

Mathematica

nn=100;
ser=Product[If[PrimePowerQ[n],1,1+x^n],{n,2,nn}];
CoefficientList[Series[ser,{x,0,nn}],x]

Formula

G.f.: Product_{k>=2, k not a prime power} 1 + x^k. - Joerg Arndt, Dec 22 2020