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


 
/Classification of numbers into abundant, perfect and deficient
/ numclass.k
 
/return 0,1 or -1 if perfect or abundant or deficient respectively
numclass: {s:(+/&~x!'!1+x)-x; :[s>x;:1;:[s<x;:-1;:0]]}
/classify numbers from 1 to 20000 into respective groups
c: =numclass' 1+!20000
/print statistics
`0: ,"Deficient = ", $(#c[0])
`0: ,"Perfect   = ", $(#c[1])
`0: ,"Abundant  = ", $(#c[2])
 