Two integers 



N


{\displaystyle N}

 and 



M


{\displaystyle M}

 are said to be amicable pairs if 



N
≠
M


{\displaystyle N\neq M}

 and the sum of the proper divisors of 



N


{\displaystyle N}

 (




s
u
m

(

p
r
o
p
D
i
v
s

(
N
)
)


{\displaystyle \mathrm {sum} (\mathrm {propDivs} (N))}

) 



=
M


{\displaystyle =M}

 as well as 




s
u
m

(

p
r
o
p
D
i
v
s

(
M
)
)
=
N


{\displaystyle \mathrm {sum} (\mathrm {propDivs} (M))=N}

.



Example

1184 and 1210 are an amicable pair, with proper divisors:

   1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592   and 
   1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605   respectively.


Task

Calculate and show here the Amicable pairs below 20,000; (there are eight).



Related tasks
 Proper divisors
 Abundant, deficient and perfect number classifications
 Aliquot sequence classifications and its amicable classification. 


with Ada.Text_IO, Generic_Divisors; use Ada.Text_IO;
 
procedure Amicable_Pairs is
 
   function Same(P: Positive) return Positive is (P);
 
   package Divisor_Sum is new Generic_Divisors
     (Result_Type => Natural, None => 0, One => Same, Add =>  "+");
 
   Num2 : Integer;
begin
   for Num1 in 4 .. 20_000 loop
      Num2 := Divisor_Sum.Process(Num1);
      if Num1 < Num2 then
	 if Num1 = Divisor_Sum.Process(Num2) then
	   Put_Line(Integer'Image(Num1) & "," & Integer'Image(Num2));
	 end if;
      end if;
   end loop;
end Amicable_Pairs;