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A320461 MM-numbers of labeled graphs with loops spanning an initial interval of positive integers. 8
1, 7, 13, 91, 161, 299, 329, 377, 611, 667, 1261, 1363, 1937, 2021, 2093, 2117, 2639, 4277, 4669, 7567, 8671, 8827, 9541, 13559, 14053, 14147, 14819, 15617, 16211, 17719, 23989, 24017, 26273, 27521, 28681, 29003, 31349, 31913, 36569, 44551, 44603, 46483, 48691 (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..43.

Eric Weisstein's World of Mathematics, Simple Graph

EXAMPLE

The sequence of terms together with their multiset multisystems begins:

     1: {}

     7: {{1,1}}

    13: {{1,2}}

    91: {{1,1},{1,2}}

   161: {{1,1},{2,2}}

   299: {{2,2},{1,2}}

   329: {{1,1},{2,3}}

   377: {{1,2},{1,3}}

   611: {{1,2},{2,3}}

   667: {{2,2},{1,3}}

  1261: {{3,3},{1,2}}

  1363: {{1,3},{2,3}}

  1937: {{1,2},{3,4}}

  2021: {{1,4},{2,3}}

  2093: {{1,1},{2,2},{1,2}}

  2117: {{1,3},{2,4}}

  2639: {{1,1},{1,2},{1,3}}

  4277: {{1,1},{1,2},{2,3}}

  4669: {{1,1},{2,2},{1,3}}

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@@(Length[primeMS[#]]==2&/@primeMS[#])]&]

CROSSREFS

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

Cf. A320456, A320458, A320459, A320462, A320532.

Sequence in context: A073220 A110455 A177952 * A132373 A110293 A253333

Adjacent sequences:  A320458 A320459 A320460 * A320462 A320463 A320464

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 13 2018

STATUS

approved

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Last modified February 20 20:08 EST 2020. Contains 332084 sequences. (Running on oeis4.)