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A084646 Hypotenuses for which there exist exactly 2 distinct integer triangles.

%I A084646 #33 Feb 16 2025 08:32:49
%S A084646 25,50,75,100,150,169,175,200,225,275,289,300,338,350,400,450,475,507,
%T A084646 525,550,575,578,600,675,676,700,775,800,825,841,867,900,950,1014,
%U A084646 1050,1075,1100,1150,1156,1175,1183,1200,1225,1350,1352,1369,1400
%N A084646 Hypotenuses for which there exist exactly 2 distinct integer triangles.
%C A084646 Numbers whose square is decomposable in 2 different ways into the sum of two nonzero squares: these are those with exactly one prime divisor of the form 4k+1 with multiplicity two. - _Jean-Christophe Hervé_, Nov 11 2013
%H A084646 Ray Chandler, <a href="/A084646/b084646.txt">Table of n, a(n) for n = 1..10000</a>
%H A084646 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>
%F A084646 Terms are obtained by the products A004144(k)*A002144(p)^2 for k, p > 0, ordered by increasing values. - _Jean-Christophe Hervé_, Nov 12 2013
%F A084646 A046080(a(n)) = 2, A046109(a(n)) = 20. - _Jean-Christophe Hervé_, Dec 01 2013
%t A084646 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]==2,AppendTo[lst,n]],{n,4*5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 12 2009 *)
%Y A084646 Cf. A002144, A006339, A046080, A046109, A083025.
%Y A084646 Cf. A004144 (0), A084645 (1), A084647 (3), A084648 (4), 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 A084646 nonn
%O A084646 1,1
%A A084646 _Eric W. Weisstein_, Jun 01 2003