A321346 Number of integer partitions of n containing no prime powers > 1.

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 5, 5, 6, 7, 8, 8, 11, 11, 14, 16, 19, 19, 25, 26, 31, 34, 40, 41, 52, 54, 63, 69, 81, 86, 105, 109, 126, 137, 160, 169, 201, 211, 242, 264, 303, 320, 375, 396, 453, 490, 557, 590, 682, 726, 823, 888, 1002, 1065, 1219

Offset

0,7

Comments

First differs from A285798 at a(30) = 52, A285798(30) = 51.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..350

Example

The a(20) = 14 integer partitions:
  (20)
  (10,10)
  (14,6)
  (18,1,1)
  (12,6,1,1)
  (6,6,6,1,1)
  (10,6,1,1,1,1)
  (15,1,1,1,1,1)
  (14,1,1,1,1,1,1)
  (12,1,1,1,1,1,1,1,1)
  (6,6,1,1,1,1,1,1,1,1)
  (10,1,1,1,1,1,1,1,1,1,1)
  (6,1,1,1,1,1,1,1,1,1,1,1,1,1,1)
  (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)

Mathematica

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

Crossrefs

Cf. A000607, A000961, A001597, A002095, A023893, A023894, A096258, A246655, A320322, A321347, A321378, A321665, A322452, A322454.

Sequence in context: A308052 A005858 A285798 * A291444 A219795 A082602

Adjacent sequences: A321343 A321344 A321345 * A321347 A321348 A321349

Keyword

nonn

Author

Gus Wiseman, Dec 11 2018

Status

approved