This ought to speed it up a little bit while being functionally equivalent:
procedure TForm.Button1Click(Sender : TObject);
var i, j, k : Integer;
begin
for i := 1 to 20 do
for j := 1 to 8765 do if (j <> i) then
for k := 1 to 5673 do if (k <> i) and (k <> j) then WriteLn(f1,
FloatToStr(RoundTo(i / 3, -2) +
IntToStr (RoundTo(j / 4, -2) +
FloatToStr(RoundTo(k / 2, -2)
);
end;
If you need more speed you could divide the workload onto several CPU cores, and stitch it together afterwards.