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: mapping
 
Integer method: properDivs -- []
    self 2 / seq  filter( #[ self swap mod 0 == ] ) ;
 
: numberClasses
| i deficient perfect s |
   0 0 ->deficient ->perfect 
   0 20000 loop: i [
      0 #+ i properDivs apply ->s
      s i <  ifTrue: [ deficient 1+ ->deficient continue ]
      s i == ifTrue: [ perfect 1+ ->perfect continue ]
      1+
      ]
   "Deficients :" . deficient .cr
   "Perfects   :" . perfect   .cr
   "Abundant   :" . .cr 
; 