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

1,1

Comments

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

Links

Table of n, a(n) for n=1..30.

Example

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

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 *)

Crossrefs

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

Sequence in context: A112042 A168307 A323566 * A008357 A259539 A138898

Adjacent sequences: A063008 A063009 A063010 * A063012 A063013 A063014

Keyword

nonn

Author

Henry Bottomley, Jul 26 2001

Status

approved