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%I A084649 #41 Jul 04 2021 13:04:20
%S A084649 3125,6250,9375,12500,18750,21875,25000,28125,34375,37500,43750,50000,
%T A084649 56250,59375,65625,68750,71875,75000,84375,87500,96875,100000,103125,
%U A084649 112500,118750,131250,134375,137500,143750,146875,150000,153125
%N A084649 Hypotenuses for which there exist exactly 5 distinct Pythagorean triangles.
%C A084649 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 A084649 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 A084649 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>
%F A084649 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 A084649 a(1) = 5^5, a(5) = 6*5^5, a(65) = 13^5. - _Jean-Christophe Hervé_, Nov 12 2013
%t A084649 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 A084649 Cf. A002144, A006339, A046080, A046109, A083025.
%Y A084649 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 A084649 nonn
%O A084649 1,1
%A A084649 _Eric W. Weisstein_, Jun 01 2003

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