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Search: id:A063011
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| A063011 |
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Ordered products of the sides of primitive Pythagorean triangles. |
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+0
6
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| 60, 780, 2040, 4200, 12180, 14760, 15540, 40260, 65520, 66780, 92820, 120120, 189840, 192720, 199980, 235620, 277680, 354960, 453960, 497640, 595140, 619020, 643500, 1021020, 1063860, 1075620, 1265880, 1484340, 1609080, 1761540
(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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EXAMPLE
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a(1)=3*4*5=60; a(2)=5*12*13=780 (rather than 6*8*10=480 which would not be primitive).
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MATHEMATICA
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k=17000000; lst={}; Do[Do[If[IntegerQ[a=Sqrt[c^2-b^2]]&&GCD[a, b, c]==1, If[a>=b, Break[]]; x=a*b*c; If[x<=k, AppendTo[lst, x]]], {b, c-1, 4, -1}], {c, 5, 700, 1}]; Union@lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 05 2009]
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CROSSREFS
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Cf. A020882, A020883, A020884, A020885, A020886, A057096.
Sequence in context: A138409 A024016 A112042 this_sequence A008357 A138898 A056321
Adjacent sequences: A063008 A063009 A063010 this_sequence A063012 A063013 A063014
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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), Jul 26 2001
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