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A063011 Ordered products of the sides of primitive Pythagorean triangles. 6
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; refs; listen; history; text; internal format)
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: A024016 A112042 A168307 * A008357 A259539 A138898

Adjacent sequences:  A063008 A063009 A063010 * A063012 A063013 A063014

KEYWORD

nonn

AUTHOR

Henry Bottomley, Jul 26 2001

STATUS

approved

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Last modified October 16 14:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)