A320458 MM-numbers of labeled simple graphs spanning an initial interval of positive integers.

1, 13, 377, 611, 1363, 1937, 2021, 2117, 16211, 17719, 26273, 27521, 44603, 56173, 58609, 83291, 91031, 91039, 99499, 141401, 143663, 146653, 147533, 153023, 159659, 167243, 170839, 203087, 237679, 243893, 265369, 271049, 276877, 290029, 301129, 315433, 467711

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 multisystem 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 multisystem with MM-number 78 is {{},{1},{1,2}}.

Links

Table of n, a(n) for n=1..37.

Eric Weisstein's World of Mathematics, Simple Graph

Example

The sequence of terms together with their multiset multisystems begins:
      1: {}
     13: {{1,2}}
    377: {{1,2},{1,3}}
    611: {{1,2},{2,3}}
   1363: {{1,3},{2,3}}
   1937: {{1,2},{3,4}}
   2021: {{1,4},{2,3}}
   2117: {{1,3},{2,4}}
  16211: {{1,2},{1,3},{1,4}}
  17719: {{1,2},{1,3},{2,3}}
  26273: {{1,2},{1,4},{2,3}}
  27521: {{1,2},{1,3},{2,4}}
  44603: {{1,2},{2,3},{2,4}}
  56173: {{1,2},{1,3},{3,4}}
  58609: {{1,3},{1,4},{2,3}}
  83291: {{1,2},{1,4},{3,4}}
  91031: {{1,3},{1,4},{2,4}}
  91039: {{1,2},{2,3},{3,4}}
  99499: {{1,3},{2,3},{2,4}}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
normQ[sys_]:=Or[Length[sys]==0, Union@@sys==Range[Max@@Max@@sys]];
Select[Range[10000], And[SquareFreeQ[#], normQ[primeMS/@primeMS[#]], And@@(And[SquareFreeQ[#], Length[primeMS[#]]==2]&/@primeMS[#])]&]

Crossrefs

Cf. A001222, A003963, A005117, A055932, A056239, A112798, A255906, A290103, A302242, A302478, A302491, A305052.

Cf. A320456, A320459, A320461, A320462, A320463.

Sequence in context: A012013 A082403 A171656 * A320635 A279306 A134498

Adjacent sequences: A320455 A320456 A320457 * A320459 A320460 A320461

Keyword

nonn

Author

Gus Wiseman, Oct 13 2018

Status

approved