cp's OEIS Frontend

A330233 Least MM-numbers of multisets of multisets with a given number of distinct representatives (obtainable by vertex-permutations).

%I A330233 #4 Dec 10 2019 12:15:22
%S A330233 1,35,141,1713,28011,355,34567,4045,54849,64615,15265,95363,126841
%N A330233 Least MM-numbers of multisets of multisets with a given number of distinct representatives (obtainable by vertex-permutations).
%C A330233 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 A330233 The sequence of terms together with their corresponding multisets of multisets begins:
%e A330233        1: {}
%e A330233       35: {{2},{1,1}}
%e A330233      141: {{1},{2,3}}
%e A330233      355: {{2},{1,1,3}}
%e A330233     1713: {{1},{2,3,4}}
%e A330233     4045: {{2},{1,1,3,4}}
%e A330233    15265: {{2},{1,4},{1,1,3}}
%e A330233    28011: {{1},{2,3,4,5}}
%e A330233    34567: {{1,2},{3,4,5}}
%e A330233    54849: {{1},{2,3},{4,5}}
%e A330233    64615: {{2},{1,1,3,4,5}}
%e A330233    95363: {{2,3},{1,1,4,5}}
%e A330233   126841: {{3},{1,2},{1,4,5}}
%t A330233 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A330233 graprms[m_]:=Union[Table[Sort[Sort/@(m/.Apply[Rule,Table[{p[[i]],i},{i,Length[p]}],{1}])],{p,Permutations[Union@@m]}]];
%t A330233 dv=Table[Length[graprms[primeMS/@primeMS[n]]],{n,1000}];
%t A330233 Table[Position[dv,i][[1,1]],{i,First/@Gather[dv]}]
%Y A330233 Sorted positions of first appearances in A330098.
%Y A330233 The unsorted version is A330230.
%Y A330233 The BII-number version is A330218.
%Y A330233 MM-numbers of achiral multisets of multisets are A330232.
%Y A330233 MM-numbers of fully-chiral multisets of multisets are A330236.
%Y A330233 Cf. A001055, A003238, A007716, A056239, A112798, A302242, A303975, A322847, A330103, A330223, A330227, A330231.
%K A330233 nonn,more
%O A330233 1,2
%A A330233 _Gus Wiseman_, Dec 09 2019