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A286224
Number of compositions (ordered partitions) of n into parts with an odd number of distinct prime divisors.
3
1, 0, 1, 1, 2, 3, 4, 8, 11, 19, 28, 47, 72, 116, 182, 289, 460, 724, 1153, 1820, 2891, 4572, 7249, 11482, 18190, 28821, 45651, 72338, 114582, 181549, 287597, 455647, 721849, 1143590, 1811753, 2870247, 4547245, 7203933, 11412922, 18080907, 28644799, 45380602, 71894401, 113899027, 180444897, 285870668
OFFSET
0,5
FORMULA
G.f.: 1/(1 - Sum_{k>=1} x^A030230(k)).
EXAMPLE
a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2].
MATHEMATICA
nmax = 45; CoefficientList[Series[1/(1 - Sum[Boole[OddQ[PrimeNu[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 04 2017
STATUS
approved