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. 


 
function Get-ProperDivisorSum ( [int]$N )
    {
    $Sum = 1
    If ( $N -gt 3 )
        {
        $SqrtN = [math]::Sqrt( $N )
        ForEach ( $Divisor1 in 2..$SqrtN )
            {
            $Divisor2 = $N / $Divisor1
            If ( $Divisor2 -is [int] ) { $Sum += $Divisor1 + $Divisor2 }
            }
        If ( $SqrtN -is [int] ) { $Sum -= $SqrtN }
        }
    return $Sum
    }
 
function Get-AmicablePairs ( $N = 300 )
    {
    ForEach ( $X in 1..$N )
        {
        $Sum = Get-ProperDivisorSum $X
        If ( $Sum -gt $X -and $X -eq ( Get-ProperDivisorSum $Sum ) )
            {
            "$X, $Sum"
            }
        }
    }
 
Get-AmicablePairs 20000
 