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%I #39 Dec 30 2019 10:40:07
%S 65,85,130,145,170,185,195,205,221,255,260,265,290,305,340,365,370,
%T 377,390,410,435,442,445,455,481,485,493,505,510,520,530,533,545,555,
%U 565,580,585,595,610,615,625,629,663,680,685,689,697,715,730,740,745
%N Hypotenuses for which there exist exactly 4 distinct integer triangles.
%C Numbers whose square is decomposable in 4 different ways into the sum of two nonzero squares: these are those with exactly 2 distinct prime divisors of the form 4k+1, each with multiplicity one, or with only one prime divisor of this form with multiplicity 4. - _Jean-Christophe Hervé_, Nov 11 2013
%C If m is a term, then 2*m and p*m are terms where p is any prime of the form 4k+3. - _Ray Chandler_, Dec 30 2019
%H Ray Chandler, <a href="/A084648/b084648.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>
%e a(1) = 65 = 5*13, and 65^2 = 52^2 + 39^2 = 56^2 + 33^2 = 60^2 + 25^2 = 63^2 + 16^2. - _Jean-Christophe Hervé_, Nov 11 2013
%t Clear[lst,f,n,i,k] f[n_]:=Module[{i=0,k=0},Do[If[Sqrt[n^2-i^2]==IntegerPart[Sqrt[n^2-i^2]],k++ ],{i,n-1,1,-1}]; k/2]; lst={}; Do[If[f[n]==4,AppendTo[lst,n]],{n,6!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 12 2009 *)
%Y Cf. A002144, A006339, A046080, A046109, A083025.
%Y Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084649 (5), A097219 (6), A097101 (7), A290499 (8), A290500 (9), A097225 (10), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A290503 (15), A097238 (16), A097239 (17), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Jun 01 2003
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