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A319270 Numbers that are 1 or whose prime indices are relatively prime and belong to the sequence, and whose prime multiplicities are also relatively prime. 1
1, 2, 6, 12, 18, 24, 26, 48, 52, 54, 72, 74, 78, 96, 104, 108, 122, 148, 156, 162, 178, 192, 202, 208, 222, 234, 244, 288, 296, 312, 338, 356, 366, 384, 404, 416, 432, 444, 446, 468, 478, 486, 488, 502, 534, 592, 606, 624, 648, 666, 702, 712, 718, 732, 746 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also Matula-Goebel numbers of series-reduced locally non-intersecting aperiodic rooted trees.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

The sequence of Matula-Goebel trees of elements of this sequence begins:

   1: o

   2: (o)

   6: (o(o))

  12: (oo(o))

  18: (o(o)(o))

  24: (ooo(o))

  26: (o(o(o)))

  48: (oooo(o))

  52: (oo(o(o)))

  54: (o(o)(o)(o))

  72: (ooo(o)(o))

  74: (o(oo(o)))

  78: (o(o)(o(o)))

  96: (ooooo(o))

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

ain[n_]:=Or[n==1, And[GCD@@primeMS[n]==1, GCD@@Length/@Split[primeMS[n]]==1, And@@ain/@primeMS[n]]];

Select[Range[100], ain]

CROSSREFS

Cf. A000081, A007097, A061775, A276625, A298748, A301700, A303431, A316470, A319271.

Sequence in context: A263082 A043343 A066080 * A071707 A069087 A304450

Adjacent sequences:  A319267 A319268 A319269 * A319271 A319272 A319273

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 16 2018

STATUS

approved

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Last modified March 18 13:47 EDT 2019. Contains 321289 sequences. (Running on oeis4.)