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 A057096 Saint-Exupéry numbers: ordered products of the three sides of Pythagorean triangles. 8

%I

%S 60,480,780,1620,2040,3840,4200,6240,7500,12180,12960,14760,15540,

%T 16320,20580,21060,30720,33600,40260,43740,49920,55080,60000,65520,

%U 66780,79860,92820,97440,97500,103680,113400,118080,120120,124320,130560,131820,164640

%N Saint-Exupéry numbers: ordered products of the three sides of Pythagorean triangles.

%C It is an open question whether any two distinct Pythagorean Triples can have the same product of their sides.

%D R. K. Guy, "Triangles with Integer Sides, Medians and Area." D21 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 188-190, 1994.

%H T. D. Noe, <a href="/A057096/b057096.txt">Table of n, a(n) for n = 1..10000</a>

%H N. des Vallieres and F. D'Agay, SCOMASE, <a href="http://www.antoinedesaintexupery.com/le-probl%C3%A8me-du-pharaon">Le Problème du Pharaon</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a>

%F a(n) = 60*A057097(n) = A057098(n)*A057099(n)*A057100(n).

%e a(1)=3*4*5=60

%t k=5000000; lst={}; Do[Do[If[IntegerQ[a=Sqrt[c^2-b^2]], If[a>=b, Break[]]; x=a*b*c; If[x<=k, AppendTo[lst,x]]], {b,c-1,4,-1}], {c,5,400,1}]; Union@lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 05 2009 *)

%Y Cf. A009004, A009012, A009111, A020886.

%K nonn

%O 1,1

%A _Henry Bottomley_, Aug 01 2000

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