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


 
abundant=0; deficient=0; perfect=0; p=[];
for N=2:20000
    K=1:ceil(N/2);
    D=K(~(rem(N, K)));
    sD=sum(D);
    if sD<N
        deficient=deficient+1;
    elseif sD==N
        perfect=perfect+1;
    else
        abundant=abundant+1;
    end
end
disp(table([deficient;perfect;abundant],'RowNames',{'Deficient','Perfect','Abundant'},'VariableNames',{'Quantities'}))
 