A063011 Ordered products of the sides of primitive Pythagorean triangles.

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

Offset: 1

Author

Henry Bottomley, Jul 26 2001

Keywords

• nonn

Comments

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

Examples

			a(1)=3*4*5=60; a(2)=5*12*13=780 (rather than 6*8*10=480, which would not be primitive).
		

Crossrefs

Cf. A020882, A020883, A020884, A020885, A020886, A057096.

Programs

Mathematica

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 *)
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 *)