|
%I #13 Oct 23 2021 21:16:56
%S 1,2,3,2,4,3,3,2,5,4,5,3,4,3,7,2,4,5,3,4,5,5,6,3,10,4,9,3,5,7,6,2,9,4,
%T 7,5,4,3,7,4,5,5,4,5,13,6,8,3,5,10,7,4,3,9,13,3,5,5,5,7,6,6,9,2,10,9,
%U 4,4,11,7,5,5,6,4,19,3,9,7,6,4,17,5,7,5
%N a(n) is the number of initial subtrees (subtrees emanating from the root) of the unlabeled rooted tree with Matula-Goebel number n.
%C We require that an initial subtree contain either all or none of the branchings under any given node.
%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%F a(1) = 1 and if n > 1 has prime factorization n = prime(x_1)^y_1 * ... * prime(x_k)^y_k then a(n) = 1 + a(x_1)^y_1 * ... * a(x_k)^y_k.
%e 70 is the Matula-Goebel number of the tree (o((o))(oo)), which has 7 distinct initial subtrees: {o, (ooo), (oo(oo)), (o(o)o), (o(o)(oo)), (o((o))o), (o((o))(oo))}. So a(70) = 7.
%t si[n_]:=If[n==1,1,1+Product[si[PrimePi[b[[1]]]]^b[[2]],{b,FactorInteger[n]}]];
%t Array[si,100]
%Y Cf. A000081, A007097, A007853, A049076, A061773, A061775, A076146, A109082, A109129, A206491, A303431, A316476, A317713.
%K nonn
%O 1,2
%A _Gus Wiseman_, Aug 13 2018
|
