A324970 Matula-Goebel numbers of rooted identity trees where not all terminal subtrees are different.

15, 30, 33, 39, 47, 55, 65, 66, 78, 87, 93, 94, 110, 113, 123, 130, 137, 141, 143, 145, 155, 165, 167, 174, 186, 195, 205, 211, 226, 235, 237, 246, 257, 274, 282, 286, 290, 303, 310, 313, 317, 319, 327, 330, 334, 339, 341, 377, 381, 390, 395, 397, 403, 410

Offset

1,1

Comments

A rooted identity tree is an unlabeled rooted tree with no repeated branches directly under the same root.

Links

Table of n, a(n) for n=1..54.

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

Formula

Complement of A324935 in A276625.

Example

The sequence of trees together with the Matula-Goebel numbers begins:
   15: ((o)((o)))
   30: (o(o)((o)))
   33: ((o)(((o))))
   39: ((o)(o(o)))
   47: (((o)((o))))
   55: (((o))(((o))))
   65: (((o))(o(o)))
   66: (o(o)(((o))))
   78: (o(o)(o(o)))
   87: ((o)(o((o))))
   93: ((o)((((o)))))
   94: (o((o)((o))))
  110: (o((o))(((o))))
  113: ((o(o)((o))))
  123: ((o)((o(o))))
  130: (o((o))(o(o)))
  137: (((o)(((o)))))
  141: ((o)((o)((o))))
  143: ((((o)))(o(o)))
  145: (((o))(o((o))))
  155: (((o))((((o)))))
  165: ((o)((o))(((o))))
  167: (((o)(o(o))))
  174: (o(o)(o((o))))
  186: (o(o)((((o)))))
  195: ((o)((o))(o(o)))

Mathematica

mgtree[n_Integer]:=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, A324971, A324978.

Sequence in context: A318992 A343337 A347455 * A033898 A051967 A162592

Adjacent sequences: A324967 A324968 A324969 * A324971 A324972 A324973

Keyword

nonn

Author

Gus Wiseman, Mar 21 2019

Status

approved