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


clear screen
 
Deficient = 0
Perfect = 0
Abundant = 0
For j=1 to 20000
	sump = sumprop(j)
	If sump < j Then
		Deficient = Deficient + 1
	ElseIf sump = j Then
		Perfect = Perfect + 1
	ElseIf sump > j Then
		Abundant = Abundant + 1
	End If
Next j
 
PRINT "Number deficient: ",Deficient
PRINT "Number perfect:   ",Perfect
PRINT "Number abundant:  ",Abundant
 
sub sumprop(num)
	local i, sum, root
 
	if num>1 then
		sum=1
		root=sqrt(num)
		for i=2 to root
			if mod(num,i) = 0 then
				sum=sum+i
				if (i*i)<>num sum=sum+num/i
			end if
		next i
	end if
	return sum
end sub