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A321936
Number of integer partitions of n containing no 1's, prime powers, or squarefree numbers.
0
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 4, 0, 1, 0, 3, 0, 2, 0, 3, 1, 1, 0, 7, 0, 2, 0, 5, 0, 5, 0, 7, 1, 3, 0, 12, 0, 4, 2, 10, 1, 8, 0, 14, 2, 6, 0, 22, 1, 10, 3, 20, 1, 15, 0, 26, 5, 12, 2
OFFSET
0,25
COMMENTS
Number of integer partitions of n using elements of A126706.
EXAMPLE
The a(56) = 7 partitions:
(56)
(28,28)
(36,20)
(44,12)
(20,18,18)
(24,20,12)
(20,12,12,12)
MATHEMATICA
nn=100;
ser=Product[If[n==1||PrimePowerQ[n]||SquareFreeQ[n], 1, 1/(1-x^n)], {n, nn}];
CoefficientList[Series[ser, {x, 0, nn}], x]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 11 2018
STATUS
approved