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 A070150 Triangular areas of integer Heronian triangles. 0
 6, 36, 66, 120, 36, 120, 120, 210, 210, 120, 300, 210, 210, 300, 378, 630, 528, 780, 528, 210, 630, 630, 300, 1176, 780, 2016, 990, 1176, 2016, 2016, 1596, 780, 1770, 528, 300, 2850, 630, 2016, 780, 990, 3240, 2016, 630 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = A070086(A070148(n)). LINKS Table of n, a(n) for n=1..43. Eric Weisstein's World of Mathematics, Heronian Triangle. R. Zumkeller, Integer-sided triangles EXAMPLE A070148(2)=368: [A070080(368), A070081(368), A070082(368)] = [9,10,17], area^2 = s*(s-9)*(s-10)*(s-17) with s=A070083(368)/2=(9+10+17)/2=18, area^2=18*9*8*1=16*81 is an integer square, therefore area=4*9=36=A000217(8). MATHEMATICA maxPerim = 300; maxSide = Floor[(maxPerim - 1)/2]; order[{a_, b_, c_}] := (a + b + c)*maxPerim^3 + a*maxPerim^2 + b*maxPerim + c; triangles = Reap[ Do[ If[ a + b + c <= maxPerim && c - b < a < c + b && b - a < c < b + a && c - a < b < c + a, Sow[{a, b, c}]], {a, 1, maxSide}, {b, a, maxSide}, {c, b, maxSide}]][[2, 1]]; stri = Sort[ triangles, order[#1] < order[#2] &]; area[{a_, b_, c_}] := With[{p = (a + b + c)/2}, Sqrt[p*(p - a)*(p - b)*(p - c)]]; triangularQ[n_] := IntegerQ[Sqrt[8*n + 1]]; area /@ Select[stri, IntegerQ[area[#]] && triangularQ[area[#]] &] (* Jean-François Alcover, Feb 22 2013 *) CROSSREFS Sequence in context: A134639 A069497 A139249 * A161144 A364586 A119845 Adjacent sequences: A070147 A070148 A070149 * A070151 A070152 A070153 KEYWORD nonn,nice AUTHOR Reinhard Zumkeller, May 05 2002 STATUS approved

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Last modified September 23 06:23 EDT 2023. Contains 365533 sequences. (Running on oeis4.)