function TryGetPerfect(x: Integer; out Value: Integer): Boolean;
var
  i, a: Integer;
begin
  i := 1;
  a := 0;

  while i <= x div 2 do
  begin
    if x mod i = 0 then
      a := a + i;
    i := i + 1;
  end;

  Result := x = a;
  if Result then
    Value := x;
end;

procedure TForm1.Button1Click(Sender: TObject);
var
  A, B, krok, hodnota: Integer;
begin
  A := StrtoInt(Edit1.Text);
  B := StrtoInt(Edit2.Text);

  Memo1.Lines.BeginUpdate;
  try
    for krok := A to B do
      if TryGetPerfect(krok, hodnota) then
        Memo1.Lines.Add(IntToStr(hodnota));
  finally
    Memo1.Lines.EndUpdate;
  end;
end;