login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 14:27 EST 2020. Contains 338724 sequences. (Running on oeis4.)