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User: Ramzan Guekhaev

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A366142 Matula-Goebel numbers of rooted trees which are symmetrical about a straight line passing through the root.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 16, 17, 18, 19, 20, 23, 25, 27, 28, 31, 32, 36, 37, 44, 45, 48, 49, 50, 53, 59, 61, 63, 64, 67, 68, 71, 72, 75, 76, 80, 81, 83, 92, 97, 98, 99, 100, 103, 107, 108, 112, 121, 124, 125, 127, 128, 131, 144, 147, 148, 151, 153, 157, 162, 169, 171, 175, 176, 180
Offset: 1

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Author

Ramzan Guekhaev and Loïc Apothéloz, Sep 30 2023

Keywords

Comments

The Matula-Goebel number of a tree is Product prime(k_i), where the k_i are the Matula-Goebel numbers of the child subtrees of the root.
A tree is symmetric about a line iff the root has 2 copies of each child subtree (one each side of the line), and an optional "middle" child subtree on the line and in turn symmetric too.

Examples

			12 is a term since it's the Matula-Goebel number of the following tree which is, per the layout shown, symmetric about the vertical.
      (*)
       |
  (*) (*) (*)
    \  |  /
     \ | /
      (*)    root

Links

Crossrefs

Cf. A000040.

Formula

a(1) = 1; k > 1 is a term iff (k/p^2 is a term for some p) OR (k = prime(j) where j is a term).

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