A317720 Numbers that are not uniform relatively prime tree numbers.

9, 12, 18, 20, 21, 23, 24, 25, 27, 28, 37, 39, 40, 44, 45, 46, 48, 49, 50, 52, 54, 56, 57, 60, 61, 63, 65, 68, 69, 71, 72, 73, 74, 75, 76, 80, 81, 83, 84, 87, 88, 89, 90, 91, 92, 96, 97, 98, 99, 103, 104, 107, 108, 111, 112, 115, 116, 117, 120, 121, 122, 124

Offset: 1

Author

Gus Wiseman, Aug 05 2018

Keywords

• nonn

Comments

A positive integer n is a uniform relatively prime tree number iff either n = 1 or n is a prime number whose prime index is a uniform relatively prime tree number, or n is a power of a squarefree number whose prime indices are relatively prime and are themselves uniform relatively prime tree numbers. A prime index of n is a number m such that prime(m) divides n.

Examples

			The sequence of non-uniform tree numbers together with their Matula-Goebel trees begins:
   9: ((o)(o))
  12: (oo(o))
  18: (o(o)(o))
  20: (oo((o)))
  21: ((o)(oo))
  23: (((o)(o)))
  24: (ooo(o))
  25: (((o))((o)))
  27: ((o)(o)(o))
  28: (oo(oo))
  37: ((oo(o)))
  39: ((o)(o(o)))
  40: (ooo((o)))
  44: (oo(((o))))
  45: ((o)(o)((o)))
		

Crossrefs

Cf. A061775, A072774, A111299, A214577, A276625, A277098, A303431, A317590.

Cf. A317705, A317707, A317708, A317709, A317710, A317712, A317717, A317718.

Programs

Mathematica

rupQ[n_]:=Or[n==1,If[PrimeQ[n],rupQ[PrimePi[n]],And[SameQ@@FactorInteger[n][[All,2]],GCD@@PrimePi/@FactorInteger[n][[All,1]]==1,And@@rupQ/@PrimePi/@FactorInteger[n][[All,1]]]]];
Select[Range[200],!rupQ[#]&]