%I
%S 1,1,3,7,21,56,174,517,1664,5383,18199
%N Number of nonisomorphic multiset partitions of weight n in which all parts are aperiodic multisets.
%C A multiset is aperiodic if its multiplicities are relatively prime.
%C The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%e Nonisomorphic representatives of the a(1) = 1 through a(4) = 21 multiset partitions with aperiodic parts:
%e {{1}} {{1,2}} {{1,2,2}} {{1,2,2,2}}
%e {{1},{1}} {{1,2,3}} {{1,2,3,3}}
%e {{1},{2}} {{1},{2,3}} {{1,2,3,4}}
%e {{2},{1,2}} {{1},{1,2,2}}
%e {{1},{1},{1}} {{1,2},{1,2}}
%e {{1},{2},{2}} {{1},{2,3,3}}
%e {{1},{2},{3}} {{1},{2,3,4}}
%e {{1,2},{3,4}}
%e {{1,3},{2,3}}
%e {{2},{1,2,2}}
%e {{3},{1,2,3}}
%e {{1},{1},{2,3}}
%e {{1},{2},{1,2}}
%e {{1},{2},{3,4}}
%e {{1},{3},{2,3}}
%e {{2},{2},{1,2}}
%e {{1},{1},{1},{1}}
%e {{1},{1},{2},{2}}
%e {{1},{2},{2},{2}}
%e {{1},{2},{3},{3}}
%e {{1},{2},{3},{4}}
%Y Cf. A000740, A000837, A007716, A007916, A100953, A301700, A303386, A303546, A303707, A303708, A303709, A303710, A320800A320810.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Nov 06 2018
