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


Module Module1
 
    Function SumProperDivisors(number As Integer) As Integer
        If number < 2 Then Return 0
        Dim sum As Integer = 0
        For i As Integer = 1 To number \ 2
            If number Mod i = 0 Then sum += i
        Next
        Return sum
    End Function
 
    Sub Main()
        Dim sum, deficient, perfect, abundant As Integer
 
        For n As Integer = 1 To 20000
            sum = SumProperDivisors(n)
            If sum < n Then
                deficient += 1
            ElseIf sum = n Then
                perfect += 1
            Else
                abundant += 1
            End If
        Next
 
        Console.WriteLine("The classification of the numbers from 1 to 20,000 is as follows : ")
        Console.WriteLine()
        Console.WriteLine("Deficient = {0}", deficient)
        Console.WriteLine("Perfect   = {0}", perfect)
        Console.WriteLine("Abundant  = {0}", abundant)
    End Sub
 
End Module