A317709 Aperiodic relatively prime tree numbers. Matula-Goebel numbers of aperiodic relatively prime trees.

1, 2, 3, 5, 6, 10, 11, 12, 13, 15, 18, 20, 22, 24, 26, 29, 30, 31, 33, 37, 40, 41, 44, 45, 47, 48, 50, 52, 54, 55, 58, 60, 61, 62, 66, 71, 72, 74, 75, 78, 79, 80, 82, 88, 89, 90, 93, 94, 96, 99, 101, 104, 108, 109, 110, 113, 116, 120, 122, 123, 124, 127, 130

Offset

1,2

Comments

A positive integer n is in the sequence iff either n = 1 or n is a prime number whose prime index already belongs to the sequence or n is not a perfect power and its prime indices are relatively prime numbers already belonging to the sequence. A prime index of n is a number m such that prime(m) divides n.

Links

Table of n, a(n) for n=1..63.

Example

The sequence of aperiodic relatively prime tree numbers together with their Matula-Goebel trees begins:
   1: o
   2: (o)
   3: ((o))
   5: (((o)))
   6: (o(o))
  10: (o((o)))
  11: ((((o))))
  12: (oo(o))
  13: ((o(o)))
  15: ((o)((o)))
  18: (o(o)(o))
  20: (oo((o)))
  22: (o(((o))))
  24: (ooo(o))
  26: (o(o(o)))
  29: ((o((o))))
  30: (o(o)((o)))
  31: (((((o)))))

Mathematica

rupQ[n_]:=Or[n==1, If[PrimeQ[n], rupQ[PrimePi[n]], And[GCD@@FactorInteger[n][[All, 2]]==1, GCD@@PrimePi/@FactorInteger[n][[All, 1]]==1, And@@rupQ/@PrimePi/@FactorInteger[n][[All, 1]]]]];
Select[Range[100], rupQ]

Crossrefs

Cf. A000081, A061775, A111299, A214577, A276625, A277098, A301700, A303431, A316503.

Cf. A317705, A317707, A317708, A317710, A317711, A317712.

Sequence in context: A014593 A261088 A303431 * A034044 A047447 A094739

Adjacent sequences: A317706 A317707 A317708 * A317710 A317711 A317712

Keyword

nonn

Author

Gus Wiseman, Aug 05 2018

Status

approved