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

Author

Gus Wiseman, Aug 07 2018

Keywords

• nonn

Comments

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

Examples

			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))))
		

Crossrefs

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

Programs

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[#]&]