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


(defn pad-class
  [n]
  (let [divs (filter #(zero? (mod n %)) (range 1 n))
        divs-sum (reduce + divs)]
    (cond
      (< divs-sum n) :deficient
      (= divs-sum n) :perfect
      (> divs-sum n) :abundant)))
 
(def pad-classes (map pad-class (map inc (range))))
 
(defn count-classes
  [n]
  (let [classes (take n pad-classes)]
    {:perfect (count (filter #(= % :perfect) classes))
     :abundant (count (filter #(= % :abundant) classes))
     :deficient (count (filter #(= % :deficient) classes))}))