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 LET nd=1: LET np=0: LET na=0
  20 FOR i=2 TO 20000
  30 LET sum=1
  40 LET max=i/2
  50 LET n=2: LET l=max-1
  60 IF n>l THEN GO TO 90
  70 IF i/n=INT (i/n) THEN LET sum=sum+n: LET max=i/n: IF max<>n THEN LET sum=sum+max: LET l=max-1
  80 LET n=n+1: GO TO 60
  90 IF sum<i THEN LET nd=nd+1: GO TO 120
 100 IF sum=i THEN LET np=np+1: GO TO 120
 110 LET na=na+1
 120 NEXT i
 130 PRINT "Number deficient: ";nd
 140 PRINT "Number perfect:   ";np
 150 PRINT "Number abundant:  ";na