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, 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

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 A367504

Adjacent sequences: A319267 A319268 A319269 * A319271 A319272 A319273

Keyword

nonn

Author

Gus Wiseman, Sep 16 2018

Status

approved