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.

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

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.

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

Under plausible assumptions about the growth of the primes, for n >= 4, a(n+1) = a(n)-th prime and A005518(n) = A057452(n-3). - David W. Wilson (davidwwilson(AT)comcast.net), Jul 09 2001

A091233(n) = (a(n)-A005517(n))+1. - Antti Karttunen (Antti.Karttunen(AT)iki.fi), May 24 2004

Apart from initial terms, same as A057452.

Cf. A061773. See A005517 for the smallest value of f(T).

Sequence in context: A128816 A006897 A034767 this_sequence A014225 A124154 A102634

Adjacent sequences: A005515 A005516 A005517 this_sequence A005519 A005520 A005521

nonn

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

More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jul 09 2001