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A286221
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Number of partitions of n into distinct parts with an even number of distinct prime divisors.
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5
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1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 4, 4, 2, 3, 4, 4, 5, 6, 5, 5, 6, 7, 9, 10, 10, 12, 11, 11, 15, 16, 15, 17, 18, 19, 23, 26, 25, 27, 30, 33, 37, 38, 39, 46, 50, 52, 57, 59, 61, 71, 77, 78, 84, 91, 97, 107, 114, 120, 131, 139, 147, 163, 172, 180, 197
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OFFSET
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0,16
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LINKS
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FORMULA
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G.f.: Product_{k>=1} (1 + x^A030231(k)).
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EXAMPLE
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a(21) = 4 because we have [21], [20, 1], [15, 6] and [14, 6, 1].
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MATHEMATICA
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nmax = 75; CoefficientList[Series[Product[1 + Boole[EvenQ[PrimeNu[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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