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

1,2

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}}.

Links

Table of n, a(n) for n=1..6.

Example

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}}

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&]]}]

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.

Sequence in context: A158586 A350205 A267565 * A330233 A220014 A157286

Adjacent sequences: A330227 A330228 A330229 * A330231 A330232 A330233

Keyword

nonn,more

Author

Gus Wiseman, Dec 09 2019

Status

approved