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A339397
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Number of partitions of n into an even number of relatively prime parts.
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1
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0, 1, 1, 2, 3, 4, 7, 9, 13, 18, 27, 32, 49, 61, 82, 106, 146, 176, 242, 293, 384, 477, 623, 744, 970, 1174, 1484, 1796, 2274, 2702, 3411, 4068, 5031, 6021, 7417, 8776, 10801, 12783, 15522, 18366, 22267, 26155, 31602, 37112, 44434, 52191, 62338, 72781, 86709, 101170
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{d|n} mu(n/d) * A027187(d).
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EXAMPLE
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a(6) = 4 because we have [5, 1], [3, 1, 1, 1], [2, 2, 1, 1] and [1, 1, 1, 1, 1, 1].
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MATHEMATICA
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Table[Sum[MoebiusMu[n/d] Length@Select[IntegerPartitions[d], EvenQ[Length@#] &], {d, Divisors[n]}], {n, 1, 50}]
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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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