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%I #4 Dec 10 2019 12:15:22
%S 1,35,141,1713,28011,355,34567,4045,54849,64615,15265,95363,126841
%N Least MM-numbers of multisets of multisets with a given number of distinct representatives (obtainable by vertex-permutations).
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}.
%e The sequence of terms together with their corresponding multisets of multisets begins:
%e 1: {}
%e 35: {{2},{1,1}}
%e 141: {{1},{2,3}}
%e 355: {{2},{1,1,3}}
%e 1713: {{1},{2,3,4}}
%e 4045: {{2},{1,1,3,4}}
%e 15265: {{2},{1,4},{1,1,3}}
%e 28011: {{1},{2,3,4,5}}
%e 34567: {{1,2},{3,4,5}}
%e 54849: {{1},{2,3},{4,5}}
%e 64615: {{2},{1,1,3,4,5}}
%e 95363: {{2,3},{1,1,4,5}}
%e 126841: {{3},{1,2},{1,4,5}}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t graprms[m_]:=Union[Table[Sort[Sort/@(m/.Apply[Rule,Table[{p[[i]],i},{i,Length[p]}],{1}])],{p,Permutations[Union@@m]}]];
%t dv=Table[Length[graprms[primeMS/@primeMS[n]]],{n,1000}];
%t Table[Position[dv,i][[1,1]],{i,First/@Gather[dv]}]
%Y Sorted positions of first appearances in A330098.
%Y The unsorted version is A330230.
%Y The BII-number version is A330218.
%Y MM-numbers of achiral multisets of multisets are A330232.
%Y MM-numbers of fully-chiral multisets of multisets are A330236.
%Y Cf. A001055, A003238, A007716, A056239, A112798, A302242, A303975, A322847, A330103, A330223, A330227, A330231.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Dec 09 2019
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