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 A096468 Perimeters of primitive Heronian triangles. 36
 12, 16, 18, 30, 32, 36, 40, 42, 44, 48, 50, 54, 56, 60, 64, 66, 68, 70, 72, 76, 78, 80, 84, 90, 96, 98, 100, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 136, 140, 144, 150, 152, 154, 156, 160, 162, 164, 168, 170, 172, 174, 176, 180, 182, 186, 190, 192, 196 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Here a primitive Heronian triangle has integer sides a,b,c with GCD(a,b,c) = 1 and integral area. The perimeter is always even. Cheney's article contains many theorems about these triangles. LINKS Peter Kagey and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Peter Kagey) Wm. Fitch Cheney, Jr., Heronian Triangles, Amer. Math. Monthly, Vol. 36, No. 1 (Jan 1929), 22-28. Eric Weisstein's World of Mathematics, Heronian Triangle EXAMPLE 12 is on this list because the triangle with sides 3, 4, 5 has integral area and perimeter 12. MATHEMATICA nn=150; lst={}; Do[s=(a+b+c)/2; If[IntegerQ[s] && GCD[a, b, c]==1, area2=s(s-a)(s-b)(s-c); If[area2>0 && IntegerQ[Sqrt[area2]], AppendTo[lst, 2s]]], {a, nn}, {b, a}, {c, b}]; Union[lst] CROSSREFS Cf. A070138 (number of primitive Heronian triangles having perimeter n), A083875 (area/6 of primitive Heronian triangles), A096467 (longest side of primitive Heronian triangles). Sequence in context: A112548 A032620 A224302 * A334983 A334984 A334338 Adjacent sequences: A096465 A096466 A096467 * A096469 A096470 A096471 KEYWORD nonn AUTHOR T. D. Noe, Jun 22 2004 EXTENSIONS Name changed by Wesley Ivan Hurt, May 17 2020 STATUS approved

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