A324978 Matula-Goebel numbers of rooted trees that are not identity trees but whose non-leaf terminal subtrees are all different.

4, 7, 8, 12, 14, 16, 17, 19, 20, 21, 24, 28, 32, 34, 35, 37, 38, 40, 42, 43, 44, 48, 51, 52, 53, 56, 57, 59, 64, 67, 68, 70, 71, 73, 74, 76, 77, 80, 84, 85, 86, 88, 89, 91, 95, 96, 102, 104, 106, 107, 112, 114, 116, 118, 124, 128, 129, 131, 133, 134, 136, 139

Offset: 1

Author

Gus Wiseman, Mar 21 2019

Keywords

• nonn

Comments

An unlabeled rooted tree is an identity tree if there are no repeated branches directly under the same root.

Examples

			The sequence of trees together with the Matula-Goebel numbers begins:
   4: (oo)
   7: ((oo))
   8: (ooo)
  12: (oo(o))
  14: (o(oo))
  16: (oooo)
  17: (((oo)))
  19: ((ooo))
  20: (oo((o)))
  21: ((o)(oo))
  24: (ooo(o))
  28: (oo(oo))
  32: (ooooo)
  34: (o((oo)))
  35: (((o))(oo))
  37: ((oo(o)))
  38: (o(ooo))
  40: (ooo((o)))
  42: (o(o)(oo))
  43: ((o(oo)))
		

Links

• Gus Wiseman, The first 36 trees together with their Matula-Goebel numbers.

Crossrefs

Cf. A000081, A004111, A007097, A196050, A276625, A317713, A324850, A324923, A324935, A324936, A324968, A324969, A324970, A324971, A324979.

Programs

Mathematica

mgtree[n_]:=If[n==1,{},mgtree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],And[!And@@Cases[mgtree[#],q:{}:>UnsameQ@@q,{0,Infinity}],UnsameQ@@Cases[mgtree[#],{},{0,Infinity}]]&]

Formula

Complement of A276625 in A324935.