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

1,4

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.

Links

Table of n, a(n) for n=1..44.

Formula

a(n) = 1 if n is prime.

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

Example

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.

Sequence in context: A287640 A322078 A019428 * A184753 A324186 A357216

Adjacent sequences: A303544 A303545 A303546 * A303548 A303549 A303550

Keyword

nonn

Author

Gus Wiseman, Apr 26 2018

Extensions

More terms from Jinyuan Wang, Jun 21 2020

Status

approved