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 A084648 Hypotenuses for which there exist exactly 4 distinct integer triangles. 31
 65, 85, 130, 145, 170, 185, 195, 205, 221, 255, 260, 265, 290, 305, 340, 365, 370, 377, 390, 410, 435, 442, 445, 455, 481, 485, 493, 505, 510, 520, 530, 533, 545, 555, 565, 580, 585, 595, 610, 615, 625, 629, 663, 680, 685, 689, 697, 715, 730, 740, 745 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers whose square is decomposable in 4 different ways into the sum of two nonzero squares: these are those with exactly 2 distinct prime divisors of the form 4k+1, each with multiplicity one, or with only one prime divisor of this form with multiplicity 4. - Jean-Christophe Hervé, Nov 11 2013 If m is a term, then 2*m and p*m are terms where p is any prime of the form 4k+3. - Ray Chandler, Dec 30 2019 LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Pythagorean Triple EXAMPLE a(1) = 65 = 5*13, and 65^2 = 52^2 + 39^2 = 56^2 + 33^2 = 60^2 + 25^2 = 63^2 + 16^2. - 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]==4, AppendTo[lst, n]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 12 2009 *) CROSSREFS Cf. A002144, A006339, A046080, A046109, A083025. Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), 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: A025303 A071011 A165158 * A224770 A274044 A024409 Adjacent sequences:  A084645 A084646 A084647 * A084649 A084650 A084651 KEYWORD nonn AUTHOR Eric W. Weisstein, Jun 01 2003 STATUS approved

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Last modified November 29 17:53 EST 2020. Contains 338769 sequences. (Running on oeis4.)