A321665 Number of strict integer partitions of n containing no 1's or prime powers.

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 0, 3, 1, 3, 2, 4, 1, 5, 2, 5, 4, 6, 4, 9, 3, 8, 7, 10, 6, 13, 7, 13, 12, 16, 10, 20, 13, 22, 19, 24, 18, 32, 23, 34, 30, 37, 30, 49, 37, 50, 47, 58, 51, 73, 58, 77, 74, 89, 80, 108, 91, 116

Offset

0,19

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..500 from Fausto A. C. Cariboni)

Formula

G.f.: Product_{k>=2, k not a prime power} 1 + x^k. - Joerg Arndt, Dec 22 2020

Example

The a(36) = 9 strict integer partitions:
  (36)
  (30,6)
  (21,15)
  (22,14)
  (24,12)
  (26,10)
  (18,12,6)
  (20,10,6)
  (14,12,10)

Mathematica

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

Crossrefs

Cf. A000607, A000961, A001597, A002095, A023893, A023894, A096258, A246655, A321346, A321347, A321378, A322452, A322454.

Sequence in context: A277486 A102395 A127504 * A329321 A334239 A335062

Adjacent sequences: A321662 A321663 A321664 * A321666 A321667 A321668

Keyword

nonn

Author

Gus Wiseman, Dec 11 2018

Status

approved