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

Author

Ilya Gutkovskiy, Dec 27 2016

Keywords

• nonn

Comments

Number of partitions of n into distinct odd prime powers (1 excluded).

Examples

			a(16) = 3 because we have [13, 3], [11, 5], [9, 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 related partition-counting sequences

Crossrefs

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

Programs

Mathematica

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

Formula

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