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

1, 35, 141, 1713, 28011, 355

Offset: 1

Author

Gus Wiseman, Dec 09 2019

Keywords

• nonn
• more

Comments

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}}.

Examples

			The sequence of terms together with their corresponding multisets of multisets begins:
      1: {}
     35: {{2},{1,1}}
    141: {{1},{2,3}}
   1713: {{1},{2,3,4}}
  28011: {{1},{2,3,4,5}}
    355: {{2},{1,1,3}}
		

Crossrefs

The BII-number version is A330218.

Positions of first appearances in A330098.

The sorted version is A330233.

MM-numbers of achiral multisets of multisets are A330232.

MM-numbers of fully-chiral multisets of multisets are A330236.

Cf. A001055, A003238, A007716, A056239, A112798, A302242, A303975, A322847, A330103, A330223, A330227, A330231, A330236.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
graprms[m_]:=Union[Table[Sort[Sort/@(m/.Apply[Rule,Table[{p[[i]],i},{i,Length[p]}],{1}])],{p,Permutations[Union@@m]}]];
dv=Table[Length[graprms[primeMS/@primeMS[n]]],{n,1000}];
Table[Position[dv,i][[1,1]],{i,First[Split[Union[dv],#1+1==#2&]]}]