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

1,1

Comments

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

Links

Table of n, a(n) for n=1..62.

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

Formula

Complement of A276625 in A324935.

Example

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)))

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}]]&]

Crossrefs

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

Sequence in context: A060833 A162967 A070286 * A047536 A093494 A310934

Adjacent sequences: A324975 A324976 A324977 * A324979 A324980 A324981

Keyword

nonn

Author

Gus Wiseman, Mar 21 2019

Status

approved