A303546 Number of non-isomorphic aperiodic multiset partitions of weight n.

1, 3, 9, 29, 90, 285, 909, 2984, 9935, 34113, 119368, 428923, 1574223, 5915235, 22699730, 89000042, 356058539, 1453069854, 6044132793, 25612564200, 110503626702, 485161228675, 2166488899641, 9835209480533, 45370059225227

Offset

1,2

Comments

A multiset is aperiodic if its multiplicities are relatively prime. For this sequence neither the parts nor their multiset union are required to be aperiodic, only the multiset of parts.

Links

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

Formula

a(n) = Sum_{d|n} mu(d) * A007716(n/d).

Example

Non-isomorphic representatives of the a(3) = 9 aperiodic multiset partitions are:
  {{1,1,1}}, {{1,2,2}}, {{1,2,3}},
  {{1},{1,1}}, {{1},{2,2}}, {{1},{2,3}}, {{2},{1,2}},
  {{1},{2},{2}}, {{1},{2},{3}}.

Crossrefs

Cf. A000740, A000837, A001055, A007716, A007916, A049311, A100953, A255906, A269134, A275024, A293993, A301700, A303386, A303431, A303547.

Sequence in context: A220950 A123947 A262253 * A135142 A195624 A098589

Adjacent sequences: A303543 A303544 A303545 * A303547 A303548 A303549

Keyword

nonn

Author

Gus Wiseman, Apr 26 2018

Status

approved