

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
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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, 23142322.
F. Goebel, On a 11correspondence between rooted trees and natural numbers, J. Combin. Theory, B 29 (1980), 141143.
I. Gutman and A. Ivic, On Matula numbers, Discrete Math., 150, 1996, 131142.
I. Gutman and YeongNan Yeh, Deducing properties of trees from their Matula numbers, Publ. Inst. Math., 53 (67), 1993, 1722.
D. Matula, A natural rooted tree enumeration by prime factorization, SIAM Rev. 10 (1968) 273.
Index entries for sequences related to MatulaGoebel 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



