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

1,2

Links

Table of n, a(n) for n=1..42.

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

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

Sequence in context: A342522 A102466 A354144 * A325202 A338973 A084176

Adjacent sequences: A322544 A322545 A322546 * A322548 A322549 A322550

Keyword

nonn,fini,full

Author

Gus Wiseman, Dec 14 2018

Status

approved