A322547 Numbers k such that every integer partition of k contains a 1, a squarefree number, or a prime power.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 59, 61, 67, 71, 79

Offset: 1

Author

Gus Wiseman, Dec 14 2018

Keywords

• nonn
• fini
• full

Examples

			48 does not belong to the sequence because there are integer partitions of 48 containing no 1's, squarefree numbers, or prime powers, namely: (48), (36,12), (28,20), (24,24), (24,12,12), (18,18,12), (12,12,12,12).
		

Crossrefs

Cf. A000607, A002095, A005117, A023893, A023894, A064573, A078135, A101417, A246655, A322546.

Programs

Mathematica

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