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. 


 
EnableExplicit
 
Procedure.i SumProperDivisors(Number)
  If Number < 2 : ProcedureReturn 0 : EndIf
  Protected i, sum = 0
  For i = 1 To Number / 2
    If Number % i = 0
      sum + i
    EndIf
  Next
  ProcedureReturn sum
EndProcedure
 
Define n, f
Define Dim sum(19999)
 
If OpenConsole()
  For n = 1 To 19999
    sum(n) = SumProperDivisors(n)
  Next
  PrintN("The pairs of amicable numbers below 20,000 are : ")
  PrintN("")
  For n = 1 To 19998
    f = sum(n)
    If f <= n Or f < 1 Or f > 19999 : Continue : EndIf
    If f = sum(n) And n = sum(f)
      PrintN(RSet(Str(n),5) + " and " + RSet(Str(sum(n)), 5))
    EndIf
  Next
  PrintN("")
  PrintN("Press any key to close the console")
  Repeat: Delay(10) : Until Inkey() <> ""
  CloseConsole()
EndIf
 