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A286220
Number of partitions of n into distinct parts with an odd number of distinct prime divisors.
4
1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 3, 5, 5, 6, 7, 7, 10, 9, 12, 12, 15, 15, 18, 19, 22, 24, 26, 30, 32, 36, 40, 43, 49, 52, 58, 63, 69, 76, 81, 91, 96, 108, 114, 127, 135, 148, 159, 173, 186, 202, 217, 234, 253, 271, 293, 313, 339, 361, 390, 416, 449, 478, 514, 547, 588, 625, 671, 714, 763, 815, 867
OFFSET
0,6
FORMULA
G.f.: Product_{k>=1} (1 + x^A030230(k)).
EXAMPLE
a(9) = 4 because we have [9], [7, 2], [5, 4] and [4, 3, 2].
MATHEMATICA
nmax = 70; CoefficientList[Series[Product[1 + Boole[OddQ[PrimeNu[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 04 2017
STATUS
approved