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%I #11 Jan 16 2023 14:37:42
%S 1,3,9,29,90,285,909,2984,9935,34113,119368,428923,1574223,5915235,
%T 22699730,89000042,356058539,1453069854,6044132793,25612564200,
%U 110503626702,485161228675,2166488899641,9835209480533,45370059225227
%N Number of non-isomorphic aperiodic multiset partitions of weight n.
%C 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.
%H Andrew Howroyd, <a href="/A303546/b303546.txt">Table of n, a(n) for n = 1..50</a>
%F a(n) = Sum_{d|n} mu(d) * A007716(n/d).
%e Non-isomorphic representatives of the a(3) = 9 aperiodic multiset partitions are:
%e {{1,1,1}}, {{1,2,2}}, {{1,2,3}},
%e {{1},{1,1}}, {{1},{2,2}}, {{1},{2,3}}, {{2},{1,2}},
%e {{1},{2},{2}}, {{1},{2},{3}}.
%Y Cf. A000740, A000837, A001055, A007716, A007916, A049311, A100953, A255906, A269134, A275024, A293993, A301700, A303386, A303431, A303547.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 26 2018