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

Author

Gus Wiseman, Apr 26 2018

Keywords

• nonn

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.

Examples

			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}}.
		

Links

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

Crossrefs

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

Formula

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