OFFSET
1,2
EXAMPLE
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).
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
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Gus Wiseman, Dec 14 2018
STATUS
approved