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


 
let mutable a=0 
let mutable b=0
let mutable c=0
let mutable d=0
let mutable e=0
let mutable f=0
for i=1 to 20000 do
    b <- 0
    f <- i/2    
    for j=1 to f do
        if i%j=0 then
           b <- b+i
    if b<i then
       c <- c+1
    if b=i then
       d <- d+1
    if b>i then
       e <- e+1
printfn " deficient %i"c
printfn "perfect %i"d
printfn "abundant %i"e
 