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.

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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).

Sequence in context: A003476 A017989 A017990 this_sequence A034063 A034073 A114623

Adjacent sequences: A005514 A005515 A005516 this_sequence A005518 A005519 A005520

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).