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 A084649 Hypotenuses for which there exist exactly 5 distinct Pythagorean triangles. 31
 3125, 6250, 9375, 12500, 18750, 21875, 25000, 28125, 34375, 37500, 43750, 50000, 56250, 59375, 65625, 68750, 71875, 75000, 84375, 87500, 96875, 100000, 103125, 112500, 118750, 131250, 134375, 137500, 143750, 146875, 150000, 153125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1019 terms from Jean-Christophe Hervé) Eric Weisstein's World of Mathematics, Pythagorean Triple FORMULA 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 EXAMPLE a(1) = 5^5, a(5) = 6*5^5, a(65) = 13^5. - Jean-Christophe Hervé, Nov 12 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]==5, AppendTo[lst, n]], {n, 3*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), 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). Sequence in context: A102709 A057067 A223184 * A169754 A016817 A115791 Adjacent sequences: A084646 A084647 A084648 * A084650 A084651 A084652 KEYWORD nonn AUTHOR Eric W. Weisstein, Jun 01 2003 STATUS approved

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Last modified June 6 12:57 EDT 2023. Contains 363142 sequences. (Running on oeis4.)