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A235122 The number of rooted trees that are isomorphic as trees to the rooted tree with Matula number n (n >=1). 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 (list; graph; refs; listen; history; text; internal format)
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.

E. Deutsch, Tree statistics from Matula numbers, arXiv preprint arXiv:1111.4288, 2011

E. 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

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

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Last modified October 18 14:48 EDT 2019. Contains 328161 sequences. (Running on oeis4.)