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

0,9

Comments

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

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

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

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

Sequence in context: A002569 A129528 A364159 * A052336 A318053 A061287

Adjacent sequences: A280197 A280198 A280199 * A280201 A280202 A280203

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 28 2016

Status

approved