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A280195
Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(k))*x^k), where omega(k) is the number of distinct prime factors (A001221).
11
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, 287596, 455647, 721847, 1143588, 1811748, 2870239, 4547232, 7203907, 11412882, 18080833, 28644680, 45380392, 71894054, 113898439, 180443915, 285869028, 452888824, 717490903, 1136687237
OFFSET
0,5
COMMENTS
Number of compositions (ordered partitions) into prime powers (1 excluded).
LINKS
FORMULA
G.f.: 1/(1 - Sum_{k>=2} floor(1/omega(k))*x^k).
EXAMPLE
a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2].
MATHEMATICA
nmax = 48; CoefficientList[Series[1/(1 - Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 28 2016
STATUS
approved