A280151 Expansion of Product_{k>=1} 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, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 23, 26, 29, 33, 37, 42, 46, 53, 58, 66, 74, 81, 91, 101, 113, 124, 139, 153, 169, 188, 207, 228, 252, 278, 304, 336, 369, 405, 444, 487, 533, 583, 640, 697, 763, 832, 908, 990, 1078, 1175, 1278

Offset

0,10

Comments

Number of partitions of n 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 related partition-counting sequences

Formula

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

Example

a(12) = 3 because we have [9, 3], [7, 5], [3, 3, 3, 3].

Mathematica

nmax = 67; CoefficientList[Series[Product[1/(1 - Floor[1/PrimeNu[2 k + 1]] x^(2 k + 1)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A001221, A018819, A023894, A061345, A246655, A280152.

Sequence in context: A018117 A086936 A214129 * A094990 A120178 A120179

Adjacent sequences: A280148 A280149 A280150 * A280152 A280153 A280154

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 27 2016

Status

approved