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A318046 a(n) is the number of initial subtrees (subtrees emanating from the root) of the unlabeled rooted tree with Matula-Goebel number n. 3
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, 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, 4, 4, 11, 7, 5, 5, 6, 4, 19, 3, 9, 7, 6, 4, 17, 5, 7, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

We require that an initial subtree contain either all or none of the branchings under any given node.

LINKS

Table of n, a(n) for n=1..84.

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

Cf. A000081, A007097, A007853, A049076, A061773, A061775, A076146, A109082, A109129, A206491, A303431, A316476, A317713.

Sequence in context: A304088 A286597 A317713 * A246348 A205782 A070296

Adjacent sequences:  A318043 A318044 A318045 * A318047 A318048 A318049

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 13 2018

STATUS

approved

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Last modified March 23 02:41 EDT 2019. Contains 321422 sequences. (Running on oeis4.)