OFFSET
1,2
COMMENTS
We require that an initial subtree contain either all or none of the branchings under any given node.
FORMULA
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.
EXAMPLE
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.
MATHEMATICA
si[n_]:=If[n==1, 1, 1+Product[si[PrimePi[b[[1]]]]^b[[2]], {b, FactorInteger[n]}]];
Array[si, 100]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 13 2018
STATUS
approved