

A084648


Hypotenuses for which there exist 4 distinct integer triangles.


19



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
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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.  JeanChristophe Hervé, Nov 11 2013


LINKS

Table of n, a(n) for n=1..51.
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.  JeanChristophe Hervé, Nov 11 2013


MATHEMATICA

Clear[lst, f, n, i, k] f[n_]:=Module[{i=0, k=0}, Do[If[Sqrt[n^2i^2]==IntegerPart[Sqrt[n^2i^2]], k++ ], {i, n1, 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, A004144, A006339, A046080, A046109.
CF. A083025, A084645, A084646, A084647, A084649.
Sequence in context: A025303 A071011 A165158 * A224770 A024409 A131574
Adjacent sequences: A084645 A084646 A084647 * A084649 A084650 A084651


KEYWORD

nonn


AUTHOR

Eric W. Weisstein, Jun 01 2003


STATUS

approved



