A280152 Expansion of Product_{k>=1} (1 + 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, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 3, 3, 3, 3, 4, 4, 5, 4, 6, 6, 6, 7, 7, 9, 8, 9, 10, 11, 12, 11, 14, 14, 16, 15, 18, 19, 19, 21, 22, 25, 25, 27, 28, 32, 32, 34, 36, 40, 41, 42, 47, 49, 52, 53, 57, 62, 63, 67, 71, 76, 79, 82, 88, 93, 98, 100, 108, 114, 118, 124

Offset

0,13

Comments

Number of partitions of n into distinct 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 related partition-counting sequences

Formula

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

Example

a(16) = 3 because we have [13, 3], [11, 5], [9, 7].

Mathematica

nmax = 78; CoefficientList[Series[Product[1 + Floor[1/PrimeNu[2 k + 1]] x^(2 k + 1), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A001221, A054685, A061345, A246655, A280151.

Sequence in context: A157235 A086289 A077807 * A281574 A191784 A261350

Adjacent sequences: A280149 A280150 A280151 * A280153 A280154 A280155

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 27 2016

Status

approved