A348067 Matula-Goebel tree number of tree n with a new leaf added below each existing vertex.

2, 6, 26, 18, 202, 78, 122, 54, 338, 606, 2462, 234, 794, 366, 2626, 162, 1346, 1014, 502, 1818, 1586, 7386, 4546, 702, 20402, 2382, 4394, 1098, 8914, 7878, 43954, 486, 32006, 4038, 12322, 3042, 2962, 1506, 10322, 5454, 12178, 4758, 4946, 22158, 34138, 13638

Offset: 1

Author

Kevin Ryde, Oct 01 2021

Keywords

• nonn

Comments

k times nested a(a(...a(1))) = A076146(k+1) is the Matula-Goebel number of the binomial tree order k constructed by an "expansion" method starting from a singleton and successively adding a new leaf under every vertex.

Examples

			tree n=6   tree a(6) = 78
  R             R___        root R
  | \           |\  \
  A  B          A @  B      new vertices
  |             |\    \     "@" below each
  C             C @    @    existing
                 \
                  @
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..5000
• Index entries for sequences related to Matula-Goebel numbers

Crossrefs

Cf. A027746 (prime factors), A076146 (binomial tree).

Cf. A297002 (add leaves under children of the root).

Programs

PARI

a(n) = my(f=factor(n)); 2*factorback([prime(self()(primepi(p))) | p<-f[,1]], f[,2]);

Formula

a(n) = 2 * Product_{i=1..k} prime(a(primepi(p[i]))), where n = p[1]*...*p[k] is the prime factorization of n with multiplicity (A027746).