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


int CntD, CntP, CntA, Num, Div, Sum;
[CntD:= 0;  CntP:= 0;  CntA:= 0;
for Num:= 1 to 20000 do
    [Sum:= if Num = 1 then 0 else 1;
    for Div:= 2 to Num-1 do
    if rem(Num/Div) = 0 then
        Sum:= Sum + Div;
    case of
      Sum < Num: CntD:= CntD+1;
      Sum > Num: CntA:= CntA+1
    other CntP:= CntP+1;
    ];
Text(0, "Deficient: ");  IntOut(0, CntD);  CrLf(0);
Text(0, "Perfect:   ");  IntOut(0, CntP);  CrLf(0);
Text(0, "Abundant:  ");  IntOut(0, CntA);  CrLf(0);
]