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 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 (list; graph; refs; listen; history; text; internal format)
 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 T. D. Noe, Table of n, a(n) for n = 1..10000 Supriya Mohanty and S. P. Mohanty, Pythagorean Numbers, Fibonacci Quarterly 28 (1990), 31-42. Eric Weisstein's World of Mathematics, Pythagorean Triple. Konstantine Hermes Zelator, A little noticed right triangle, arXiv: 0804.1340 [math.GM]. FORMULA a(n) = A057102(n) / 4. - Max Alekseyev, Nov 14 2008 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 Cf. A009112, A002144, A003273, A046081, A057102, A024365. Sequence in context: A334788 A332962 A132398 * A147778 A209452 A275302 Adjacent sequences:  A073117 A073118 A073119 * A073121 A073122 A073123 KEYWORD easy,nonn AUTHOR Zak Seidov, Aug 25 2002 EXTENSIONS Description corrected by James R. Buddenhagen, Aug 10 2008, and by Max Alekseyev, Nov 12 2008 Edited by N. J. A. Sloane, Apr 06 2015 STATUS approved

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Last modified July 3 08:14 EDT 2020. Contains 335417 sequences. (Running on oeis4.)