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


  [ 0 swap witheach + ]        is sum ( [ --> n )
 
  [ factors -1 pluck 
    dip sum 
    2dup = iff
      [ 2drop 1 ] done
    < iff 0 else 2 ]           is dpa ( n --> n )
 
  0 0 0
  20000 times 
    [ i 1+ dpa 
      [ table
        [ 1+ ]
        [ dip 1+ ]
        [ rot 1+ unrot ] ] do ]
  say "Deficient = " echo cr
  say "  Perfect = " echo cr
  say " Abundant = " echo cr