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


            NORMAL MODE IS INTEGER
            DIMENSION P(20000)
            MAX = 20000
            THROUGH INIT, FOR I=1, 1, I.G.MAX
INIT        P(I) = 0
            THROUGH CALC, FOR I=1, 1, I.G.MAX/2
            THROUGH CALC, FOR J=I+I, I, J.G.MAX
CALC        P(J) = P(J)+I
            DEF = 0
            PER = 0
            AB = 0
            THROUGH CLSFY, FOR N=1, 1, N.G.MAX
            WHENEVER P(N).L.N, DEF = DEF+1
            WHENEVER P(N).E.N, PER = PER+1
CLSFY       WHENEVER P(N).G.N, AB = AB+1
            PRINT FORMAT FDEF,DEF
            PRINT FORMAT FPER,PER
            PRINT FORMAT FAB,AB
            VECTOR VALUES FDEF = $I5,S1,9HDEFICIENT*$
            VECTOR VALUES FPER = $I5,S1,7HPERFECT*$
            VECTOR VALUES FAB =  $I5,S1,8HABUNDANT*$
            END OF PROGRAM 