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A111299 Numbers n such that the Matula tree of n is a binary tree (i.e., root has degree 2 and all nodes except root and leaves have degree 3). 33
4, 14, 49, 86, 301, 454, 886, 1589, 1849, 3101, 3986, 6418, 9761, 13766, 13951, 19049, 22463, 26798, 31754, 48181, 51529, 57026, 75266, 85699, 93793, 100561, 111139, 128074, 137987, 196249, 199591, 203878, 263431, 295969, 298154, 302426, 426058, 448259, 452411 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..186

Keith Briggs, Matula numbers and rooted trees

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

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

Index entries for sequences related to Matula-Goebel numbers

FORMULA

The Matula tree of n is defined by as follows (p_m denotes the m-th prime):

matula(n):

... create a node labeled n

... for each prime factor m of n:

...... add the subtree matula(p_m), by an edge labeled m

... return the node

MATHEMATICA

nn=20000;

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

binQ[n_]:=Or[n===1, With[{m=primeMS[n]}, And[Length[m]===2, And@@binQ/@m]]];

Select[Range[2, nn], binQ] (* Gus Wiseman, Aug 28 2017 *)

PROG

(PARI) i(n)=n==2 || is(primepi(n))

is(n)=if(n<14, return(n==4)); my(f=factor(n), t=#f[, 1]); if(t>1, t==2 && f[1, 2]==1 && f[2, 2]==1 && i(f[1, 1]) && i(f[2, 1]), f[1, 2]==2 && i(f[1, 1])) \\ Charles R Greathouse IV, Mar 29 2013

(PARI) list(lim)=my(v=List(), t); forprime(p=2, sqrt(lim), t=p; forprime(q=p, lim\t, if(i(p)&&i(q), listput(v, t*q)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Mar 29 2013

CROSSREFS

Cf. A000081, A001190, A005517, A005518, A007097, A061773, A245824.

Sequence in context: A047028 A220819 A047138 * A245824 A110686 A071729

Adjacent sequences:  A111296 A111297 A111298 * A111300 A111301 A111302

KEYWORD

nonn

AUTHOR

Keith Briggs (keith.briggs(AT)bt.com), Nov 02 2005

EXTENSIONS

Definition corrected by Charles R Greathouse IV, Mar 29 2013

a(27)-a(39) from Charles R Greathouse IV, Mar 29 2013

STATUS

approved

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)