A084646 Hypotenuses for which there exist exactly 2 distinct integer triangles.

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

Offset

1,1

Comments

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

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Pythagorean Triple

Formula

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

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]==2, 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), 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

Keyword

nonn

Author

Eric W. Weisstein, Jun 01 2003

Status

approved