1,2

Let p(1)=2, ... denote the primes. The label f(T) for a rooted tree T is 1 if T has 1 node, otherwise f(T) = Product p(f(T_i)) where the T_i are the subtrees obtained by deleting the root and the edges adjacent to it.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

F. Goebel, On a 1-1-correspondence between rooted trees and natural numbers, J. Combin. Theory, B 29 (1980), 141-143.

I. Gutman and A. Ivic, On Matula numbers, Discrete Math., 150, 1996, 131-142.

D. W. Matula, A natural rooted tree enumeration by prime factorization, SIAM Review, 10, 1968, 273.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

a(n+3) = 5*a(n) for n >= 3 under plausible assumptions about growth of prime numbers. - David W. Wilson, Jul 05, 2001.

A091233(n) = (A005518(n)-a(n))+1. - Antti Karttunen (Antti.Karttunen(AT)iki.fi), May 24 2004

A005517:=(-1-2*z-3*z**2+z**4)/(-1+5*z**3); [Conjectured by S. Plouffe in his 1992 dissertation.]

Cf. A061773. See A005518 for the largest value of f(T).

Adjacent sequences: A005514 A005515 A005516 this_sequence A005518 A005519 A005520

Sequence in context: A003476 A017989 A017990 this_sequence A034063 A034073 A114623

nonn,easy,nice

njas