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


open monad io number list
 
divisors n = filter ((0 ==) << (n `mod`)) [1 .. (n `div` 2)] 
classOf n = compare (sum $ divisors n) n
 
do
  let classes = map classOf [1 .. 20000]
  let printRes w c = putStrLn $ w ++ (show << length $ filter (== c) classes)
  printRes "deficient: " LT
  printRes "perfect:   " EQ
  printRes "abundant:  " GT