These define three classifications of positive integers based on their   proper divisors.

Let   P(n)   be the sum of the proper divisors of   n   where the proper divisors are all positive divisors of   n   other than   n   itself.

   if    P(n) <  n    then  n  is classed as  deficient  (OEIS A005100).
   if    P(n) == n    then  n  is classed as  perfect    (OEIS A000396).
   if    P(n) >  n    then  n  is classed as  abundant   (OEIS A005101).



Example

6   has proper divisors of   1,   2,   and   3.

1 + 2 + 3 = 6,   so   6   is classed as a perfect number.



Task

Calculate how many of the integers   1   to   20,000   (inclusive) are in each of the three classes.

Show the results here.



Related tasks

   Aliquot sequence classifications.   (The whole series from which this task is a subset.)
   Proper divisors
   Amicable pairs


 
function Get-ProperDivisorSum ( [int]$N )
    {
    If ( $N -lt 2 ) { return 0 }
 
    $Sum = 1
    If ( $N -gt 3 )
        {
        $SqrtN = [math]::Sqrt( $N )
        ForEach ( $Divisor in 2..$SqrtN )
            {
            If ( $N % $Divisor -eq 0 ) { $Sum += $Divisor + $N / $Divisor }
            }
        If ( $N % $SqrtN -eq 0 ) { $Sum -= $SqrtN }
        }
    return $Sum
    }
 
 
$Deficient = $Perfect = $Abundant = 0
 
ForEach ( $N in 1..20000 )
    {
    Switch ( [math]::Sign( ( Get-ProperDivisorSum $N ) - $N ) )
        {
        -1 { $Deficient++ }
         0 { $Perfect++   }
         1 { $Abundant++  }
        }
    }
 
"Deficient: $Deficient"
"Perfect  : $Perfect"
"Abundant : $Abundant"
 