

A330230


Least MMnumber of a multiset of multisets with n distinct representatives obtainable by permuting the vertices.


13




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 MMnumber 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 MMnumber 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 BIInumber version is A330218.
Positions of first appearances in A330098.
The sorted version is A330233.
MMnumbers of achiral multisets of multisets are A330232.
MMnumbers of fullychiral 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



