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-th row has A000081(n) terms.

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

The labels for the rooted trees with at most 4 nodes are as follows (x is the root):

................................o

................................|

..........o.......o.......o...o.o

..........|........\.......\./..|

..o.o...o.o.o.o.o...o...o...o...o

..|..\./..|..\|/.....\./....|...|

x.x...x...x...x.......x.....x...x

1.2...4...3...8.......6.....7...5 (label)

Triangle begins:

1;

2;

3,4;

5,6,7,8;

9,10,11,12,13,14,16,17,19;

15,18,20,21,22,23,24,26,28,29,31,32,34,37,38,41,43,53,59,67;

25,27,30,33,35,36,39,40,42,44,46,47,48,49,51,52,56,57,58,61,62,64,68,\

71,73,74,76,79,82,83,86,89,101,106,107,109,118,127,131,134,139,157,163,\

179,191,241,277,331;

...

Cf. A061775. Minimal and maximal entries in each row give A005517, A005518.

Sequence in context: A075592 A070776 A076564 this_sequence A125007 A035062 A032964

Adjacent sequences: A061770 A061771 A061772 this_sequence A061774 A061775 A061776

nonn,tabf,nice,easy

N. J. A. Sloane (njas(AT)research.att.com), Jun 22 2001

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 01 2004