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A321378
Number of integer partitions of n containing no 1's or prime powers.
7
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 3, 0, 3, 2, 3, 0, 6, 1, 5, 3, 6, 1, 11, 2, 9, 6, 12, 5, 19, 4, 17, 11, 23, 9, 32, 10, 31, 22, 39, 17, 55, 21, 57, 37, 67, 33, 92, 44, 97, 65, 114, 63, 154, 78, 162, 113, 191, 117, 250, 138, 269, 194, 320
OFFSET
0,13
EXAMPLE
The a(30) = 11 integer partitions:
(30)
(24,6)
(15,15)
(18,12)
(20,10)
(18,6,6)
(12,12,6)
(14,10,6)
(10,10,10)
(12,6,6,6)
(6,6,6,6,6)
MATHEMATICA
nn=100;
ser=Product[If[PrimePowerQ[n], 1, 1/(1-x^n)], {n, 2, nn}];
CoefficientList[Series[ser, {x, 0, nn}], x]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 11 2018
STATUS
approved