

A073120


Areas of Pythagorean (or right) triangles with integer sides of the form (2mn, m^2  n^2, m^2 + n^2).


10



6, 24, 30, 60, 84, 96, 120, 180, 210, 240, 330, 336, 384, 480, 486, 504, 546, 630, 720, 840, 924, 960, 990, 1224, 1320, 1344, 1386, 1536, 1560, 1710, 1716, 1920, 1944, 2016, 2184, 2310, 2340, 2430, 2520, 2574, 2730, 2880, 3036, 3360, 3570, 3696, 3750, 3840
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OFFSET

1,1


COMMENTS

Equivalently, integers of the form m*n*(m^2  n^2) where m,n are positive integers with m > n.  James R. Buddenhagen, Aug 10 2008
The sequence giving the areas of all Pythagorean triangles is A009112 (sometimes called "Pythagorean numbers").
For example, the sequence does not contain 54, the area of the Pythagorean triangle with sides (9,12,15).  Robert Israel, Apr 03 2015
See also Theorem 2 of Mohanty and Mohanty.  T. D. Noe, Sep 24 2013


LINKS



FORMULA



EXAMPLE

6 = 3*4/2 is the area of the right triangle with sides 3 and 4.
84 = 7*24/2 is the area of the right triangle with sides 7 and 24.


MATHEMATICA

nn = 16; t = Union[Flatten[Table[m*n*(m^2  n^2), {m, 2, nn}, {n, m  1}]]]; Select[t, # < nn*(nn^2  1) &]


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



