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

%I A348066 #14 Feb 13 2022 23:18:10
%S A348066 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,
%T A348066 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,
%U A348066 3,58,11,30,13,62,3,2,65,66,5,10,15,30,29,6,5,26
%N A348066 Matula-Goebel tree number of tree n with all duplicate sibling subtrees reduced to one copy of each.
%C A348066 Here a subtree means a vertex and all its descendants (children, grandchildren, etc.).
%C A348066 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.
%C A348066 Or equivalently, duplicates among sibling subtrees are considered after each subtree has itself been reduced.
%C A348066 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.
%C A348066 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).
%H A348066 Kevin Ryde, <a href="/A348066/b348066.txt">Table of n, a(n) for n = 1..10000</a>
%H A348066 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A348066 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%F A348066 a(n) = Product of distinct prime(a(primepi(p))), over p the prime factors of n.
%e A348066 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.
%e A348066   tree n=42    tree a(42) = 6
%e A348066       R___         R         root R
%e A348066      / \  \        | \
%e A348066     A   B  C       A  C
%e A348066     |   |\         |
%e A348066     D   E F        D
%o A348066 (PARI) a(n) = vecprod(Set([prime(self()(primepi(p))) | p<-factor(n)[,1]]));
%Y A348066 Cf. A276625 (asymmetric trees), A007947.
%K A348066 nonn
%O A348066 1,2
%A A348066 _Kevin Ryde_, Oct 01 2021