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 A055595 Area of congruent triangles with integer sides and positive integer area, ordered by longest side, then second longest side and finally shortest side. 11
 6, 12, 12, 24, 48, 30, 60, 54, 24, 84, 48, 36, 60, 120, 108, 66, 42, 96, 84, 126, 60, 108, 192, 90, 150, 84, 168, 120, 36, 204, 240, 210, 210, 60, 120, 216, 132, 300, 96, 336, 72, 192, 144, 240, 480, 294, 84, 252, 360, 432, 114, 156, 180, 210, 420, 120, 210, 420 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 FORMULA a(n) = sqrt(s(n)*(s(n)-A055592(n))*(s(n)-A055593(n))*(s(n)-A055594(n))) where s(n) = (A055592(n)+A055593(n)+A055594(n))/2 i.e. half the perimeter of the triangle MATHEMATICA max = 42; triangles = Reap[Do[s = (a+b+c)/2; area = Sqrt[s*(s-a)*(s-b)*(s-c)]; If[IntegerQ[area] && area > 0, Sow[{a, b, c, area}]], {a, 1, max}, {b, a, max}, {c, b, max}]][[2, 1]]; A055595 = Sort[triangles, #1[[3]]*max^2 + #1[[2]]*max + #1[[1]] < #2[[3]]* max^2 + #2[[2]]*max + #2[[1]] &][[All, 4]](* Jean-François Alcover, Jun 12 2012 *) CROSSREFS Cf. A055592, A055593, A055594. Sequence in context: A330921 A183688 A298016 * A132632 A223352 A063648 Adjacent sequences:  A055592 A055593 A055594 * A055596 A055597 A055598 KEYWORD nonn AUTHOR Henry Bottomley, May 26 2000 STATUS approved

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)