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A084646
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Hypotenuses for which there exist exactly 2 distinct integer triangles.
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30
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25, 50, 75, 100, 150, 169, 175, 200, 225, 275, 289, 300, 338, 350, 400, 450, 475, 507, 525, 550, 575, 578, 600, 675, 676, 700, 775, 800, 825, 841, 867, 900, 950, 1014, 1050, 1075, 1100, 1150, 1156, 1175, 1183, 1200, 1225, 1350, 1352, 1369, 1400
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Ray Chandler, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pythagorean Triple
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FORMULA
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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
A046080(a(n)) = 2, A046109(a(n)) = 20. - Jean-Christophe Hervé, Dec 01 2013
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A002144, A006339, A046080, A046109, A083025.
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).
Sequence in context: A043350 A023723 A044458 * A031472 A045210 A169860
Adjacent sequences: A084643 A084644 A084645 * A084647 A084648 A084649
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KEYWORD
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nonn
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AUTHOR
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Eric W. Weisstein, Jun 01 2003
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STATUS
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approved
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