OFFSET
1,3
COMMENTS
The label f(T) for a rooted tree T is 1 if T has 1 node, otherwise f(T) = Product_{T_i} prime(f(T_i)) where the T_i are the subtrees obtained by deleting the root and the edges adjacent to it. (Cf. A061773 for illustration.)
LINKS
EXAMPLE
a(7) = 2 because the rooted tree with Matula-Goebel number 7 is the rooted tree Y.
a(2^m) = 1 because the rooted tree with Matula-Goebel number 2^m is the star tree with m edges.
MATHEMATICA
MGTree[n_]:=If[n==1, {}, MGTree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Count[MGTree[n], _[__], {0, Infinity}], {n, 100}] (* Gus Wiseman, Nov 28 2022 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
François Marques, Mar 14 2021
STATUS
approved