A348066 Matula-Goebel tree number of tree n with all duplicate sibling subtrees reduced to one copy of each.

1, 2, 3, 2, 5, 6, 3, 2, 3, 10, 11, 6, 13, 6, 15, 2, 5, 6, 3, 10, 3, 22, 5, 6, 5, 26, 3, 6, 29, 30, 31, 2, 33, 10, 15, 6, 13, 6, 39, 10, 41, 6, 13, 22, 15, 10, 47, 6, 3, 10, 15, 26, 3, 6, 55, 6, 3, 58, 11, 30, 13, 62, 3, 2, 65, 66, 5, 10, 15, 30, 29, 6, 5, 26

Offset

1,2

Comments

Here a subtree means a vertex and all its descendants (children, grandchildren, etc.).

Any subtree which is a duplicate of a sibling subtree is deleted and this is repeated until no duplicates exist. The order of deletions does not affect the result.

Or equivalently, duplicates among sibling subtrees are considered after each subtree has itself been reduced.

The resulting tree a(n) has no duplicates, which means asymmetric so that a(n) is a term of A276625. Reduction is no-change a(n) = n if and only if n is in A276625.

This sequence is a divisibility sequence since the prime factors of a(m*n) are the union of the prime factors of a(m) and a(n), so that a(m*n) is divisible by a(n).

Links

Kevin Ryde, Table of n, a(n) for n = 1..10000

Index to divisibility sequences

Index entries for sequences related to Matula-Goebel numbers

Formula

a(n) = Product of distinct prime(a(primepi(p))), over p the prime factors of n.

Example

In the following tree n=42, E and F are (singleton) subtrees of B and are the same so reduce to E alone. With that change, subtrees A,D and B,E are the same, so reduce to A,D alone.
  tree n=42    tree a(42) = 6
      R___         R         root R
     / \  \        | \
    A   B  C       A  C
    |   |\         |
    D   E F        D

Prog

(PARI) a(n) = vecprod(Set([prime(self()(primepi(p))) | p<-factor(n)[, 1]]));

Crossrefs

Cf. A276625 (asymmetric trees), A007947.

Sequence in context: A066119 A003970 A094443 * A227071 A276270 A349668

Adjacent sequences: A348063 A348064 A348065 * A348067 A348068 A348069

Keyword

nonn

Author

Kevin Ryde, Oct 01 2021

Status

approved