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 "/math" for Int, Nums
 
var d = 0
var a = 0
var p = 0
for (i in 1..20000) {
    var j = Nums.sum(Int.properDivisors(i))
    if (j < i) {
        d = d + 1
    } else if (j == i) {
        p = p + 1
    } else {
        a = a + 1
    }
}
System.print("There are %(d) deficient numbers between 1 and 20000")
System.print("There are %(a) abundant numbers  between 1 and 20000")
System.print("There are %(p) perfect numbers between 1 and 20000")