This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A068969 #14 Feb 16 2025 08:32:45
%S A068969 6,210,528,1680,1800,5304,6930,3150,4650,21000,32760,69342,53550,
%T A068969 2170560,2200200,2501070,646800,4777080,4796550,11865840,12243840,
%U A068969 12863760,18064200,30510480,3232320,66023100,70691400,47977380,144357720,185560830,156128700,320843040
%N A068969 Areas of integer Heronian triangles [A068967(n), prime(A068967(n)), A068968(n)].
%H A068969 Giovanni Resta, <a href="/A068969/b068969.txt">Table of n, a(n) for n = 1..120</a>
%H A068969 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>.
%H A068969 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeronsFormula.html">Heron's Formula</a>.
%e A068969 a(5) = 37: [37, A000040(37), A068968(5)] = [37,157,130], with s = (36+157+130)/2 = 162: Area^2 = s*(s-37)*(s-157)*(s-130) = 162*125*5*32 = 3240000 = 1800*1800, therefore a(5) = 1800.
%t A068969 area[{a_, b_, c_}] := Block[{s = (a + b + c)/2}, Sqrt[s (s-a) (s-b) (s-c)]]; zz[n_] := Block[{s, p = Prime[n], t, z, A}, s = Solve[(n^2 - 2 n p + p^2 - z) (z - n^2 - 2 n p - p^2) == t^2 && z>0 && t>0, {t, z}, Integers]; If[s == {}, {}, z = Sort@ Select[Sqrt[z /. s], IntegerQ]]; Select[Table[{n, p, e}, {e, z}], IntegerQ[A = area[#]] && A > 0 &]]; area /@ Join @@ Parallelize@ Array[zz, 4300] (* _Giovanni Resta_, Apr 20 2020 *)
%Y A068969 Cf. A046131, A055595, A068966.
%K A068969 nonn
%O A068969 1,1
%A A068969 _Reinhard Zumkeller_, Mar 30 2002
%E A068969 Erroneous term 25070627 removed and more terms from _Giovanni Resta_, Apr 20 2020