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


F sum_proper_divisors(n)
   R I n < 2 {0} E sum((1 .. n I/ 2).filter(it -> (@n % it) == 0))
 
V deficient = 0
V perfect = 0
V abundant = 0
 
L(n) 1..20000
   V sp = sum_proper_divisors(n)
   I sp < n
      deficient++
   E I sp == n
      perfect++
   E I sp > n
      abundant++
 
print(‘Deficient = ’deficient)
print(‘Perfect   = ’perfect)
print(‘Abundant  = ’abundant)