A303547 Number of non-isomorphic periodic multiset partitions of weight n.

0, 1, 1, 4, 1, 13, 1, 33, 10, 94, 1, 327, 1, 913, 100, 3017, 1, 10233, 1, 34236, 919, 119372, 1, 432234, 91, 1574227, 9945, 5916177, 1, 22734231, 1, 89003059, 119378, 356058543, 1000, 1453509039, 1, 6044132797, 1574233, 25612601420, 1, 110509543144, 1, 485161348076

Offset: 1

Author

Gus Wiseman, Apr 26 2018

Keywords

• nonn

Comments

A multiset is periodic if its multiplicities have a common divisor greater than 1. For this sequence neither the parts nor their multiset union are required to be periodic, only the multiset of parts.

Examples

			Non-isomorphic representatives of the a(4) = 4 multiset partitions are {{1,1},{1,1}}, {{1,2},{1,2}}, {{1},{1},{1},{1}}, {{1},{1},{2},{2}}.
		

Crossrefs

Cf. A000740, A000837, A001055, A007716, A007916, A049311, A100953, A255906, A269134, A275024, A293993, A301700, A303386, A303431, A303546.

Formula

a(n) = 1 if n is prime.

a(n) = A007716(n) - A303546(n).

Extensions

More terms from Jinyuan Wang, Jun 21 2020