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A280200 Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(2*k-1))*x^(2*k-1)), where omega() is the number of distinct prime factors (A001221). 2
1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 11, 16, 21, 26, 37, 47, 61, 84, 108, 143, 191, 249, 331, 437, 575, 763, 1004, 1326, 1754, 2311, 3055, 4036, 5323, 7033, 9288, 12257, 16193, 21379, 28223, 37278, 49212, 64984, 85815, 113297, 149614, 197551, 260839, 344439, 454795, 600517, 792958, 1047023, 1382519, 1825533, 2410456, 3182845 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
Number of compositions (ordered partitions) into odd prime powers (1 excluded).
LINKS
Eric Weisstein's World of Mathematics, Prime Power
FORMULA
G.f.: 1/(1 - Sum_{k>=2} floor(1/omega(2*k-1))*x^(2*k-1)).
EXAMPLE
a(10) = 3 because we have [7, 3], [5, 5] and [3, 7].
MATHEMATICA
nmax = 60; CoefficientList[Series[1/(1 - Sum[Floor[1/PrimeNu[2 k - 1]] x^(2 k - 1), {k, 2, nmax}]), {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A002569 A129528 A364159 * A052336 A318053 A061287
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 28 2016
STATUS
approved

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Last modified March 3 03:04 EST 2024. Contains 370499 sequences. (Running on oeis4.)