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

1,2

Links

Table of n, a(n) for n=1..13.

Example

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).

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

Crossrefs

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

Sequence in context: A341089 A056781 A079446 * A283262 A334393 A115975

Adjacent sequences: A322543 A322544 A322545 * A322547 A322548 A322549

Keyword

nonn,fini,full

Author

Gus Wiseman, Dec 14 2018

Status

approved