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%I #25 Mar 07 2017 11:22:38
%S 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,
%T 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,
%U 6,7,5,4,6,4,6,4,7
%N The number of rooted trees that are isomorphic as trees to the rooted tree with Matula number n (n >=1).
%C a(n) is the number of entries in row n of the triangle A235121.
%H E. Deutsch, <a href="http://arxiv.org/abs/1111.4288">Tree statistics from Matula numbers</a>, arXiv preprint arXiv:1111.4288, 2011
%H E. Deutsch, <a href="http://dx.doi.org/10.1016/j.dam.2012.05.012">Rooted tree statistics from Matula numbers</a>, Discrete Appl. Math., 160, 2012, 2314-2322.
%H F. Goebel, <a href="http://dx.doi.org/10.1016/0095-8956(80)90049-0">On a 1-1-correspondence between rooted trees and natural numbers</a>, J. Combin. Theory, B 29 (1980), 141-143.
%H I. Gutman and A. Ivic, <a href="http://dx.doi.org/10.1016/0012-365X(95)00182-V">On Matula numbers</a>, Discrete Math., 150, 1996, 131-142.
%H I. Gutman and Yeong-Nan Yeh, <a href="http://www.emis.de/journals/PIMB/067/3.html">Deducing properties of trees from their Matula numbers</a>, Publ. Inst. Math., 53 (67), 1993, 17-22.
%H D. Matula, <a href="http://www.jstor.org/stable/2027327?seq=30">A natural rooted tree enumeration by prime factorization</a>, SIAM Rev. 10 (1968) 273.
%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%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(nops(M(j)), j = 1 .. 100); # _W. Edwin Clark_
%Y Cf. A235121.
%K nonn
%O 1,3
%A _Emeric Deutsch_, Jan 19 2014
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