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).

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

Offset: 0

Author

Ilya Gutkovskiy, Dec 28 2016

Keywords

• nonn

Comments

Number of compositions (ordered partitions) into odd prime powers (1 excluded).

Examples

			a(10) = 3 because we have [7, 3], [5, 5] and [3, 7].
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Prime Power
• Index entries for sequences related to compositions

Crossrefs

Cf. A001221, A023359, A061345, A246655, A280151, A280195.

Programs

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]

Formula

G.f.: 1/(1 - Sum_{k>=2} floor(1/omega(2*k-1))*x^(2*k-1)).