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A320459 MM-numbers of labeled multigraphs spanning an initial interval of positive integers. 8
1, 13, 169, 377, 611, 1363, 1937, 2021, 2117, 2197, 4901, 7943, 10933, 16211, 17719, 25181, 26273, 27521, 28561, 28717, 39527, 44603, 56173, 58609, 61393, 63713, 64061, 83291, 86903, 91031, 91039, 94987, 99499, 103259, 141401, 142129, 143663, 146653, 147533 (list; graph; refs; listen; history; text; internal format)
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..39.

Eric Weisstein's World of Mathematics, Simple Graph

EXAMPLE

The sequence of terms together with their multiset multisystems begins:

      1: {}

     13: {{1,2}}

    169: {{1,2},{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}}

   2197: {{1,2},{1,2},{1,2}}

   4901: {{1,2},{1,2},{1,3}}

   7943: {{1,2},{1,2},{2,3}}

  10933: {{1,2},{1,3},{1,3}}

  16211: {{1,2},{1,3},{1,4}}

  17719: {{1,2},{1,3},{2,3}}

  25181: {{1,2},{1,2},{3,4}}

  26273: {{1,2},{1,4},{2,3}}

  27521: {{1,2},{1,3},{2,4}}

  28561: {{1,2},{1,2},{1,2},{1,2}}

  28717: {{1,2},{2,3},{2,3}}

  39527: {{1,3},{1,3},{2,3}}

  44603: {{1,2},{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[100000], And[normQ[primeMS/@primeMS[#]], And@@(And[SquareFreeQ[#], Length[primeMS[#]]==2]&/@primeMS[#])]&]

CROSSREFS

Cf. A003963, A055932, A056239, A112798, A255906, A290103, A302242, A302478, A305052, A305078.

Cf. A320456, A320458, A320461, A320462, A320464.

Sequence in context: A223655 A207685 A207511 * A207343 A207892 A207882

Adjacent sequences:  A320456 A320457 A320458 * A320460 A320461 A320462

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 13 2018

STATUS

approved

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Last modified January 25 04:34 EST 2022. Contains 350565 sequences. (Running on oeis4.)