cp's OEIS Frontend

A330230 Least MM-number of a multiset of multisets with n distinct representatives obtainable by permuting the vertices.

%I A330230 #4 Dec 10 2019 12:15:15
%S A330230 1,35,141,1713,28011,355
%N A330230 Least MM-number of a multiset of multisets with n distinct representatives obtainable by permuting the vertices.
%C A330230 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 A330230 The sequence of terms together with their corresponding multisets of multisets begins:
%e A330230       1: {}
%e A330230      35: {{2},{1,1}}
%e A330230     141: {{1},{2,3}}
%e A330230    1713: {{1},{2,3,4}}
%e A330230   28011: {{1},{2,3,4,5}}
%e A330230     355: {{2},{1,1,3}}
%t A330230 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A330230 graprms[m_]:=Union[Table[Sort[Sort/@(m/.Apply[Rule,Table[{p[[i]],i},{i,Length[p]}],{1}])],{p,Permutations[Union@@m]}]];
%t A330230 dv=Table[Length[graprms[primeMS/@primeMS[n]]],{n,1000}];
%t A330230 Table[Position[dv,i][[1,1]],{i,First[Split[Union[dv],#1+1==#2&]]}]
%Y A330230 The BII-number version is A330218.
%Y A330230 Positions of first appearances in A330098.
%Y A330230 The sorted version is A330233.
%Y A330230 MM-numbers of achiral multisets of multisets are A330232.
%Y A330230 MM-numbers of fully-chiral multisets of multisets are A330236.
%Y A330230 Cf. A001055, A003238, A007716, A056239, A112798, A302242, A303975, A322847, A330103, A330223, A330227, A330231, A330236.
%K A330230 nonn,more
%O A330230 1,2
%A A330230 _Gus Wiseman_, Dec 09 2019