Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Jun 21 2020 05:39:16
%S 0,1,1,4,1,13,1,33,10,94,1,327,1,913,100,3017,1,10233,1,34236,919,
%T 119372,1,432234,91,1574227,9945,5916177,1,22734231,1,89003059,119378,
%U 356058543,1000,1453509039,1,6044132797,1574233,25612601420,1,110509543144,1,485161348076
%N Number of non-isomorphic periodic multiset partitions of weight n.
%C 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.
%F a(n) = 1 if n is prime.
%F a(n) = A007716(n) - A303546(n).
%e 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}}.
%Y Cf. A000740, A000837, A001055, A007716, A007916, A049311, A100953, A255906, A269134, A275024, A293993, A301700, A303386, A303431, A303546.
%K nonn
%O 1,4
%A _Gus Wiseman_, Apr 26 2018
%E More terms from _Jinyuan Wang_, Jun 21 2020