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


10 DEFINT A-Z: LM=20000
20 DIM P(LM)
30 FOR I=1 TO LM: P(I)=-32767: NEXT
40 FOR I=1 TO LM/2: FOR J=I+I TO LM STEP I: P(J)=P(J)+I: NEXT: NEXT
50 FOR I=1 TO LM
60 X=I-32767
70 IF P(I)<X THEN D=D+1 ELSE IF P(I)=X THEN P=P+1 ELSE A=A+1
80 NEXT
90 PRINT "DEFICIENT:";D
100 PRINT "PERFECT:";P
110 PRINT "ABUNDANT:";A