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A321665 Number of strict integer partitions of n containing no 1's or prime powers. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)