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 A084647 Hypotenuses for which there exist exactly 3 distinct integer triangles. 31
 125, 250, 375, 500, 750, 875, 1000, 1125, 1375, 1500, 1750, 2000, 2197, 2250, 2375, 2625, 2750, 2875, 3000, 3375, 3500, 3875, 4000, 4125, 4394, 4500, 4750, 4913, 5250, 5375, 5500, 5750, 5875, 6000, 6125, 6591, 6750, 7000, 7125, 7375, 7750 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers whose square is decomposable in 3 different ways into the sum of two nonzero squares: these are those with exactly one prime divisor of the form 4k+1 with multiplicity three. - Jean-Christophe Hervé, Nov 11 2013 LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1140 terms from Jean-Christophe Hervé) Eric Weisstein's World of Mathematics, Pythagorean Triple FORMULA Terms are obtained by the products A004144(k)*A002144(p)^3 for k, p > 0, ordered by increasing values. - Jean-Christophe Hervé, Nov 12 2013 EXAMPLE a(1) = 125 = 5^3, and 125^2 = 100^2 + 75^2 = 117^2 + 44^2 = 120^2 + 35^2. - Jean-Christophe Hervé, Nov 11 2013 MATHEMATICA 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]==3, AppendTo[lst, n]], {n, 4*5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 12 2009 *) CROSSREFS Cf. A002144, A006339, A046080, A046109, A083025. Cf. A004144 (0), A084645 (1), A084646 (2), 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: A029782 A043351 A023724 * A031473 A045214 A045199 Adjacent sequences: A084644 A084645 A084646 * A084648 A084649 A084650 KEYWORD nonn AUTHOR Eric W. Weisstein, Jun 01 2003 STATUS approved

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Last modified September 27 10:45 EDT 2023. Contains 365688 sequences. (Running on oeis4.)