A321378 Number of integer partitions of n containing no 1's or prime powers.

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 3, 0, 3, 2, 3, 0, 6, 1, 5, 3, 6, 1, 11, 2, 9, 6, 12, 5, 19, 4, 17, 11, 23, 9, 32, 10, 31, 22, 39, 17, 55, 21, 57, 37, 67, 33, 92, 44, 97, 65, 114, 63, 154, 78, 162, 113, 191, 117, 250, 138, 269, 194, 320

Offset

0,13

Links

Table of n, a(n) for n=0..70.

Example

The a(30) = 11 integer partitions:
  (30)
  (24,6)
  (15,15)
  (18,12)
  (20,10)
  (18,6,6)
  (12,12,6)
  (14,10,6)
  (10,10,10)
  (12,6,6,6)
  (6,6,6,6,6)

Mathematica

nn=100;
ser=Product[If[PrimePowerQ[n], 1, 1/(1-x^n)], {n, 2, nn}];
CoefficientList[Series[ser, {x, 0, nn}], x]

Crossrefs

Cf. A000607, A000688, A000961, A002095, A023893, A023894, A096258, A246655, A320322, A321346, A321347, A321665, A322452, A322454.

Sequence in context: A363859 A328458 A099362 * A307039 A243046 A058940

Adjacent sequences: A321375 A321376 A321377 * A321379 A321380 A321381

Keyword

nonn

Author

Gus Wiseman, Dec 11 2018

Status

approved