A348067 - OEIS

%I #12 Oct 12 2021 07:58:51

%S 2,6,26,18,202,78,122,54,338,606,2462,234,794,366,2626,162,1346,1014,

%T 502,1818,1586,7386,4546,702,20402,2382,4394,1098,8914,7878,43954,486,

%U 32006,4038,12322,3042,2962,1506,10322,5454,12178,4758,4946,22158,34138,13638

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

%C 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.

%H Kevin Ryde, <a href="/A348067/b348067.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>

%F 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).

%e tree n=6   tree a(6) = 78

%e   R             R___        root R

%e   | \           |\  \

%e   A  B          A @  B      new vertices

%e   |             |\    \     "@" below each

%e   C             C @    @    existing

%e                  \

%e                   @

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

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

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

%K nonn

%O 1,1

%A _Kevin Ryde_, Oct 01 2021