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A339398
Number of partitions of n into an odd number of relatively prime parts.
1
1, 0, 1, 1, 3, 3, 7, 8, 14, 16, 28, 31, 51, 58, 85, 103, 150, 171, 247, 289, 391, 468, 631, 737, 981, 1160, 1496, 1784, 2290, 2684, 3430, 4050, 5054, 5991, 7445, 8750, 10835, 12741, 15560, 18328, 22315, 26100, 31658, 37058, 44497, 52111, 62415, 72708, 86801, 101063
OFFSET
1,5
COMMENTS
Moebius transform of A027193.
FORMULA
a(n) = Sum_{d|n} mu(n/d) * A027193(d).
EXAMPLE
a(6) = 3 because we have [4, 1, 1], [3, 2, 1] and [2, 1, 1, 1, 1].
MATHEMATICA
Table[Sum[MoebiusMu[n/d] Length@Select[IntegerPartitions[d], OddQ[Length@#] &], {d, Divisors[n]}], {n, 1, 50}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 02 2020
STATUS
approved