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%I #11 Jun 08 2018 19:49:13
%S 60,780,2040,4200,12180,14760,15540,40260,65520,66780,92820,120120,
%T 189840,192720,199980,235620,277680,354960,453960,497640,595140,
%U 619020,643500,1021020,1063860,1075620,1265880,1484340,1609080,1761540
%N Ordered products of the sides of primitive Pythagorean triangles.
%C It is an open question whether any two distinct Pythagorean triples can have the same product of their sides.
%e a(1)=3*4*5=60; a(2)=5*12*13=780 (rather than 6*8*10=480, which would not be primitive).
%t 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 (* _Vladimir Joseph Stephan Orlovsky_, Sep 05 2009 *)
%t With[{nn=50},Take[(Times@@#)Sqrt[#[[1]]^2+#[[2]]^2]&/@Union[Sort/@ ({Times@@#, (Last[#]^2-First[#]^2)/2}&/@(Select[Subsets[Range[1,nn+1,2],{2}],GCD@@#==1&]))]//Union,nn]] (* _Harvey P. Dale_, Jun 08 2018 *)
%Y Cf. A020882, A020883, A020884, A020885, A020886, A057096.
%K nonn
%O 1,1
%A _Henry Bottomley_, Jul 26 2001