login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A257539 The smallest of the Matula numbers of the rooted trees that are isomorphic as trees to the rooted tree with Matula number n. 1

%I #8 Mar 07 2017 11:24:21

%S 1,2,3,3,5,5,7,7,9,9,9,12,12,12,15,16,12,18,16,20,20,15,18,24,25,18,

%T 27,28,20,30,15,32,25,20,35,36,24,24,30,40,18,42,28,35,45,27,30,48,49,

%U 50,35,42,32,54,55,56,40,30,20,60,36,25,63,64,65,65,24,49,45,70,40

%N The smallest of the Matula numbers of the rooted trees that are isomorphic as trees to the rooted tree with Matula number n.

%C The Matula number of a rooted tree can be defined in the following recursive manner: to the one-vertex tree there corresponds the number 1; to a tree T with root degree 1 there corresponds the t-th prime number, where t is the Matula number of the tree obtained from T by deleting the edge emanating from the root; to a tree T with root degree m>=2 there corresponds the product of the Matula numbers of the m branches of T.

%D E. Deutsch, Rooted tree statistics from Matula numbers, Discrete Applied Math., 160, 2012, 2314-2322.

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

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

%D I. Gutman and Y-N. Yeh, Deducing properties of trees from their Matula numbers, Publ. Inst. Math., 53 (67), 1993, 17-22.

%D J. L. Martin, M. Morin, J. D. Wagner, On distinguishing trees by their chromatic symmetric functions, J. Combin. Theory, A115, 2008, 237-253.

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

%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>

%F a(n) = first entry in row n of A235121. The Maple program is based on this.

%e a(4) = 3. Indeed the rooted tree corresponding to the Matula number 4 is \/ . It is isomorphic as a tree only to itself and to the path tree P(3), rooted at one of its end-vertex; the Matula number of this tree is 3; min {3,4} = 3.

%e a(14)=12 because the Matula numbers of the rooted trees isomorphic as a tree to the rooted tree having Matula number 14 are: 12, 13, 14, and 17.

%p with(numtheory): f := proc (m) local x, p, S: S := NULL: x := factorset(m): for p in x do S := S, ithprime(m/p)*pi(p) end do: S end proc: M := proc (m) local A, B: A := {m}: do B := A: A := `union`(map(f, A), A): if B = A then return A end if end do end proc: seq(M(j)[1], j = 1 .. 100);

%Y Cf. A235121.

%K nonn

%O 1,2

%A _Emeric Deutsch_, May 02 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)