login
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).
4
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).
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 27 2016
STATUS
approved