%I A096468
%S A096468 12,16,18,30,32,36,40,42,44,48,50,54,56,60,64,66,68,70,72,76,78,80,84,
%T A096468 90,96,98,100,104,108,110,112,114,120,126,128,130,132,136,140,144,150,
%U A096468 152,154,156,160,162,164,168,170,172,174,176,180,182,186,190,192,196
%N A096468 Numbers n that can be the perimeter of a primitive Heronian triangle.
%C A096468 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.
%D A096468 Wm. Fitch Cheney, Jr., Heronian Triangles, Amer. Math. Monthly, Vol. 
               36, No. 1 (Jan 1929), 22-28.
%H A096468 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HeronianTriangle.html">Heronian Triangle</a>
%e A096468 12 is on this list because the triangle with sides 3, 4, 5 has integral 
               area and perimeter 12.
%t A096468 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]
%Y A096468 Cf. A070138 (number of primitive Heronian triangles having perimeter 
               n), A083875 (area/6 of primitive Heronian triangles), A096467 (longest 
               side of primitive Heronian triangles).
%Y A096468 Sequence in context: A089021 A112548 A032620 this_sequence A054281 A070329 
               A064695
%Y A096468 Adjacent sequences: A096465 A096466 A096467 this_sequence A096469 A096470 
               A096471
%K A096468 nonn
%O A096468 1,1
%A A096468 T. D. Noe (noe(AT)sspectra.com), Jun 22 2004