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%I #41 Jul 04 2021 13:04:20
%S 3125,6250,9375,12500,18750,21875,25000,28125,34375,37500,43750,50000,
%T 56250,59375,65625,68750,71875,75000,84375,87500,96875,100000,103125,
%U 112500,118750,131250,134375,137500,143750,146875,150000,153125
%N Hypotenuses for which there exist exactly 5 distinct Pythagorean triangles.
%C Numbers whose square is decomposable in 5 different ways into the sum of two nonzero squares: these are those with exactly one prime divisor of the form 4k+1 with multiplicity 5. - _Jean-Christophe Hervé_, Nov 12 2013
%H Ray Chandler, <a href="/A084649/b084649.txt">Table of n, a(n) for n = 1..10000</a> (first 1019 terms from Jean-Christophe Hervé)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>
%F Terms are obtained by the products A004144(k)*A002144(p)^5 for k, p > 0 ordered by increasing values. - _Jean-Christophe Hervé_, Nov 12 2013
%e a(1) = 5^5, a(5) = 6*5^5, a(65) = 13^5. - _Jean-Christophe Hervé_, Nov 12 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]==5,AppendTo[lst,n]],{n,3*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), A084648 (4), 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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