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A290137
Number of compositions (ordered partitions) of n into nonprime squarefree parts (A000469).
1
1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 22, 30, 41, 55, 73, 96, 128, 173, 235, 317, 426, 570, 763, 1023, 1375, 1848, 2484, 3337, 4482, 6017, 8077, 10843, 14562, 19560, 26276, 35292, 47392, 63632, 85443, 114741, 154098, 206957, 277941, 373254, 501244, 673121, 903945, 1213935, 1630246, 2189330
OFFSET
0,7
FORMULA
G.f.: 1/(1 - Sum_{k>=1} x^A000469(k)).
EXAMPLE
a(8) = 4 because we have [6, 1, 1], [1, 6, 1], [1, 1, 6] and [1, 1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
nmax = 53; CoefficientList[Series[1/(1 - Sum[Boole[SquareFreeQ[k] && PrimeNu[k] != 1] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 20 2017
STATUS
approved