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


use ntheory qw/divisor_sum/;
my @type = <Perfect Abundant Deficient>;
say join "\n", map { sprintf "%2d %s", $_, $type[divisor_sum($_)-$_ <=> $_] } 1..12;
my %h;
$h{divisor_sum($_)-$_ <=> $_}++ for 1..20000;
say "Perfect: $h{0}    Deficient: $h{-1}    Abundant: $h{1}";