A322546 Numbers k such that every integer partition of k contains a 1 or a prime power.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 19, 23

Offset: 1

Author

Gus Wiseman, Dec 14 2018

Keywords

• nonn
• fini
• full

Examples

			24 does not belong to the sequence because there are integer partitions of 24 containing no 1's or prime powers, namely: (24), (18,6), (14,10), (12,12), (12,6,6), (6,6,6,6).
		

Crossrefs

Cf. A000607, A002095, A023893, A023894, A064573, A078135, A101417, A246655, A320322, A322452, A322454, A322547.

Programs

Mathematica

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