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A321347
Number of strict integer partitions of n containing no prime powers (including 1).
5
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
OFFSET
0,16
COMMENTS
First differs from A286221 at a(30) = 6, A286221(30) = 5.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..500
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 11 2018
STATUS
approved