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A342507 Number of internal nodes in rooted tree with Matula-Goebel number n. 1
0, 1, 2, 1, 3, 2, 2, 1, 3, 3, 4, 2, 3, 2, 4, 1, 3, 3, 2, 3, 3, 4, 4, 2, 5, 3, 4, 2, 4, 4, 5, 1, 5, 3, 4, 3, 3, 2, 4, 3, 4, 3, 3, 4, 5, 4, 5, 2, 3, 5, 4, 3, 2, 4, 6, 2, 3, 4, 4, 4, 4, 5, 4, 1, 5, 5, 3, 3, 5, 4, 4, 3, 4, 3, 6, 2, 5, 4, 5, 3, 5, 4, 5, 3, 5, 3, 5, 4, 3, 5, 4, 4, 6, 5, 4, 2, 6, 3, 6, 5 (list; graph; refs; listen; history; text; internal format)
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

François Marques, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Matula-Goebel numbers

FORMULA

a(1)=0 and a(n) = A061775(n) - A109129(n) for n > 1.

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.

PROG

(PARI) A342507(n) = if( n==1, 0, my(f=factor(n)); 1+sum(k=1, matsize(f)[1], A342507(primepi(f[k, 1]))*f[k, 2]));

CROSSREFS

Cf. A061775, A196050, A109129.

Sequence in context: A306467 A157810 A072339 * A261337 A337195 A260088

Adjacent sequences:  A342504 A342505 A342506 * A342508 A342509 A342510

KEYWORD

nonn

AUTHOR

François Marques, Mar 14 2021

STATUS

approved

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Last modified October 16 16:20 EDT 2021. Contains 348042 sequences. (Running on oeis4.)