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


import java.util.stream.LongStream;
 
public class NumberClassifications {
 
    public static void main(String[] args) {
        int deficient = 0;
        int perfect = 0;
        int abundant = 0;
 
        for (long i = 1; i <= 20_000; i++) {
            long sum = properDivsSum(i);
            if (sum < i)
                deficient++;
            else if (sum == i)
                perfect++;
            else
                abundant++;
        }
        System.out.println("Deficient: " + deficient);
        System.out.println("Perfect: " + perfect);
        System.out.println("Abundant: " + abundant);
    }
 
    public static long properDivsSum(long n) {
        return LongStream.rangeClosed(1, (n + 1) / 2).filter(i -> n != i && n % i == 0).sum();
    }
}