This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057096 Saint-Exupery numbers: ordered products of the three sides of Pythagorean triangles. 8


%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-Exupery 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.saint-exupery.org/home/fr_inv_math1.htm">Le Probleme 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 03:50 EST 2015. Contains 264554 sequences.