

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).


2



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



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 partitioncounting 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



