A235122 The number of rooted trees that are isomorphic as trees to the rooted tree with Matula number n (n >=1).

1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 3, 2, 4, 4, 2, 5, 5, 3, 4, 4, 4, 4, 3, 2, 5, 7, 3, 2, 4, 5, 6, 4, 4, 4, 7, 5, 4, 6, 2, 6, 6, 3, 7, 4, 3, 5, 6, 6, 2, 4, 4, 4, 5, 7, 5, 7, 4, 4, 5, 2, 8, 8, 4, 3, 6, 7, 5, 4, 6, 4, 6, 4, 7

Offset

1,3

Comments

a(n) is the number of entries in row n of the triangle A235121.

Links

Table of n, a(n) for n=1..77.

Emeric Deutsch, Tree statistics from Matula numbers, arXiv preprint arXiv:1111.4288 [math.CO], 2011.

Emeric Deutsch, Rooted tree statistics from Matula numbers, Discrete Appl. Math., 160, 2012, 2314-2322.

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.

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

D. Matula, A natural rooted tree enumeration by prime factorization, SIAM Rev. 10 (1968) 273.

Index entries for sequences related to Matula-Goebel numbers

Maple

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(nops(M(j)), j = 1 .. 100); # W. Edwin Clark

Mathematica

f[m_] := Prime[m/#]*PrimePi[#]& /@ FactorInteger[m][[All, 1]];
M[m_] := Module[{A, B}, A = {m}; While[True, B = A; A = Union[Map[f, A] // Flatten, A] // DeleteCases[#, 0]&; If[B == A, Return[A]]]];
Table[M[j] // Length, {j, 1, 100}] (* Jean-François Alcover, Sep 14 2024, after W. Edwin Clark *)

Crossrefs

Cf. A235121.

Sequence in context: A064661 A226982 A280952 * A131996 A090618 A186444

Adjacent sequences: A235119 A235120 A235121 * A235123 A235124 A235125

Keyword

nonn

Author

Emeric Deutsch, Jan 19 2014

Status

approved