A317789 Matula-Goebel numbers of rooted trees that are not locally nonintersecting.

9, 21, 23, 25, 27, 39, 46, 49, 57, 63, 65, 69, 73, 81, 83, 87, 91, 92, 97, 103, 111, 115, 117, 121, 125, 129, 133, 138, 146, 147, 159, 161, 166, 167, 169, 171, 183, 184, 185, 189, 194, 199, 203, 206, 207, 213, 219, 227, 230, 235, 237, 243, 247, 249, 253, 259

Offset

1,1

Comments

An unlabeled rooted tree is locally nonintersecting if there is no common subbranch to all branches directly under any given node.

Links

Table of n, a(n) for n=1..56.

Example

The sequence of rooted trees that are not locally nonintersecting together with their Matula-Goebel numbers begins:
   9: ((o)(o))
  21: ((o)(oo))
  23: (((o)(o)))
  25: (((o))((o)))
  27: ((o)(o)(o))
  39: ((o)(o(o)))
  46: (o((o)(o)))
  49: ((oo)(oo))
  57: ((o)(ooo))
  63: ((o)(o)(oo))
  65: (((o))(o(o)))
  69: ((o)((o)(o)))
  73: (((o)(oo)))
  81: ((o)(o)(o)(o))
  83: ((((o)(o))))
  87: ((o)(o((o))))
  91: ((oo)(o(o)))
  92: (oo((o)(o)))
  97: ((((o))((o))))

Mathematica

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

Crossrefs

Cf. A000081, A184155, A276625, A316470, A316495, A316502, A317785, A317786, A317787.

Sequence in context: A251219 A284131 A111171 * A333039 A266000 A067887

Adjacent sequences: A317786 A317787 A317788 * A317790 A317791 A317792

Keyword

nonn

Author

Gus Wiseman, Aug 07 2018

Status

approved