A321347 Number of strict integer partitions of n containing no prime powers (including 1).

1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 4, 4, 2, 3, 4, 4, 5, 6, 5, 6, 7, 7, 9, 10, 10, 13, 12, 11, 15, 17, 16, 19, 20, 20, 25, 28, 26, 30, 33, 35, 41, 43, 42, 50, 55, 57, 64, 67, 67, 79, 86, 87, 97, 105, 109, 124, 131, 135, 151, 163, 169

Offset

0,16

Comments

First differs from A286221 at a(30) = 6, A286221(30) = 5.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500

Example

The a(36) = 13 strict integer partitions:
  (36),
  (21,15), (22,14), (24,12), (26,10), (30,6), (35,1),
  (14,12,10), (18,12,6), (20,10,6), (20,15,1), (21,14,1),
  (15,14,6,1).

Mathematica

nn=100;
ser=Product[If[PrimePowerQ[n], 1, 1+x^n], {n, nn}];
CoefficientList[Series[ser, {x, 0, nn}], x]

Crossrefs

Cf. A000607, A000961, A001597, A002095, A023893, A023894, A096258, A246655, A320322, A321346, A321378, A321665, A322452, A322454.

Sequence in context: A289494 A029286 A286221 * A324383 A342789 A050333

Adjacent sequences: A321344 A321345 A321346 * A321348 A321349 A321350

Keyword

nonn

Author

Gus Wiseman, Dec 11 2018

Status

approved