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Search: id:A057096
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| A057096 |
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Saint-Exupery numbers: ordered products of the three sides of Pythagorean triangles. |
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+0
8
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| 60, 480, 780, 1620, 2040, 3840, 4200, 6240, 7500, 12180, 12960, 14760, 15540, 16320, 20580, 21060, 30720, 33600, 40260, 43740, 49920, 55080, 60000, 65520, 66780, 79860, 92820, 97440, 97500, 103680, 113400, 118080, 120120, 124320
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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It is an open question whether any two distinct Pythagorean Triples can have the same product of their sides.
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REFERENCES
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
N. des Vallieres and F. D'Agay, SCOMASE, Le Probleme du Pharaon
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FORMULA
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a(n) =60*A057097(n) =A057098(n)*A057099(n)*A057100(n)
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EXAMPLE
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a(1)=3*4*5=60
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MATHEMATICA
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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 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 05 2009]
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CROSSREFS
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Cf. A009004, A009012, A009111, A020886.
Sequence in context: A020868 A088943 A097387 this_sequence A069140 A101384 A081384
Adjacent sequences: A057093 A057094 A057095 this_sequence A057097 A057098 A057099
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Aug 01 2000
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