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

Author

Gus Wiseman, Aug 05 2018

Keywords

• nonn

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.

Examples

			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)))))
		

Crossrefs

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

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

Programs

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]