OFFSET
1,1
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..120
Eric Weisstein's World of Mathematics, Heronian Triangle.
Eric Weisstein's World of Mathematics, Heron's Formula.
EXAMPLE
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 30 2002
EXTENSIONS
Erroneous term 25070627 removed and more terms from Giovanni Resta, Apr 20 2020
STATUS
approved