A317711 Numbers that are not uniform tree numbers.

12, 18, 20, 24, 28, 37, 40, 44, 45, 48, 50, 52, 54, 56, 60, 61, 63, 68, 71, 72, 74, 75, 76, 80, 84, 88, 89, 90, 92, 96, 98, 99, 104, 107, 108, 111, 112, 116, 117, 120, 122, 124, 126, 132, 135, 136, 140, 142, 144, 147, 148, 150, 152, 153, 156, 157, 160, 162

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..58.

Example

The sequence of non-uniform tree numbers together with their Matula-Goebel trees begins:
  12: (oo(o))
  18: (o(o)(o))
  20: (oo((o)))
  24: (ooo(o))
  28: (oo(oo))
  37: ((oo(o)))
  40: (ooo((o)))
  44: (oo(((o))))
  45: ((o)(o)((o)))
  48: (oooo(o))
  50: (o((o))((o)))
  52: (oo(o(o)))
  54: (o(o)(o)(o))
  56: (ooo(oo))
  60: (oo(o)((o)))

Mathematica

rupQ[n_]:=Or[n==1, And[SameQ@@FactorInteger[n][[All, 2]], And@@rupQ/@PrimePi/@FactorInteger[n][[All, 1]]]];
Select[Range[100], !rupQ[#]&]

Crossrefs

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

Cf. A317705, A317707, A317708, A317709, A317710 (complement), A317712, A317717, A317718.

Sequence in context: A370409 A363101 A369516 * A359890 A323055 A059404

Adjacent sequences: A317708 A317709 A317710 * A317712 A317713 A317714

Keyword

nonn

Author

Gus Wiseman, Aug 05 2018

Status

approved