A339397 Number of partitions of n into an even number of relatively prime parts.

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

Offset

1,4

Comments

Moebius transform of A027187.

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) * A027187(d).

Example

a(6) = 4 because we have [5, 1], [3, 1, 1, 1], [2, 2, 1, 1] and [1, 1, 1, 1, 1, 1].

Mathematica

Table[Sum[MoebiusMu[n/d] Length@Select[IntegerPartitions[d], EvenQ[Length@#] &], {d, Divisors[n]}], {n, 1, 50}]

Crossrefs

Cf. A000837, A027187, A339398.

Sequence in context: A005576 A339592 A241131 * A129373 A139078 A065046

Adjacent sequences: A339394 A339395 A339396 * A339398 A339399 A339400

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 02 2020

Status

approved