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A286218
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Number of partitions of n into parts with an odd number of prime divisors (counted with multiplicity).
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4
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1, 0, 1, 1, 1, 2, 2, 3, 4, 4, 6, 7, 9, 11, 13, 16, 19, 23, 28, 33, 40, 46, 55, 65, 76, 89, 104, 121, 141, 163, 190, 219, 253, 290, 334, 383, 439, 502, 573, 653, 744, 845, 961, 1089, 1234, 1395, 1576, 1780, 2007, 2259, 2544, 2856, 3209, 3598, 4033, 4516, 5051, 5644, 6304, 7033, 7843
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OFFSET
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0,6
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LINKS
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FORMULA
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G.f.: Product_{k>=1} 1/(1 - x^A026424(k)).
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EXAMPLE
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a(8) = 4 because we have [8], [5, 3], [3, 3, 2] and [2, 2, 2, 2].
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MAPLE
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with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
`if`(bigomega(d)::odd, d, 0), d=divisors(j)), j=1..n)/n)
end:
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MATHEMATICA
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nmax = 60; CoefficientList[Series[Product[1/(1 - Boole[OddQ[PrimeOmega[k]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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