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A321347 Number of strict integer partitions of n containing no prime powers (including 1). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,16

COMMENTS

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

LINKS

Table of n, a(n) for n=0..71.

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 A050333 A271775

Adjacent sequences:  A321344 A321345 A321346 * A321348 A321349 A321350

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 11 2018

STATUS

approved

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Last modified May 26 04:46 EDT 2019. Contains 323579 sequences. (Running on oeis4.)