A339398 Number of partitions of n into an odd number of relatively prime parts.

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.

Links

Table of n, a(n) for n=1..50.

Index entries for sequences related to partitions

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

Cf. A000837, A027193, A339397.

Sequence in context: A161416 A241637 A241641 * A241414 A218568 A218569

Adjacent sequences: A339395 A339396 A339397 * A339399 A339400 A339401

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 02 2020

Status

approved