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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). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 19 22:04 EST 2018. Contains 299357 sequences. (Running on oeis4.)