A321347 Number of strict integer partitions of n containing no prime powers (including 1).

1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 4, 4, 2, 3, 4, 4, 5, 6, 5, 6, 7, 7, 9, 10, 10, 13, 12, 11, 15, 17, 16, 19, 20, 20, 25, 28, 26, 30, 33, 35, 41, 43, 42, 50, 55, 57, 64, 67, 67, 79, 86, 87, 97, 105, 109, 124, 131, 135, 151, 163, 169

Offset: 0

Author

Gus Wiseman, Dec 11 2018

Keywords

• nonn

Comments

First differs from A286221 at a(30) = 6, A286221(30) = 5.

Examples

			The a(36) = 13 strict integer partitions:
  (36),
  (21,15), (22,14), (24,12), (26,10), (30,6), (35,1),
  (14,12,10), (18,12,6), (20,10,6), (20,15,1), (21,14,1),
  (15,14,6,1).
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000607, A000961, A001597, A002095, A023893, A023894, A096258, A246655, A320322, A321346, A321378, A321665, A322452, A322454.

Programs

Mathematica

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