user
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
assistant
(formerly Perl 6)

**Works with**: rakudo version 2018.12

```
sub propdivsum (\x) {
    my @l = 1 if x > 1;
    (2 .. x.sqrt.floor).map: -> \d {
        unless x % d { @l.push: d; my \y = x div d; @l.push: y if y != d }
    }
    sum @l
}

say bag (1..20000).map: { propdivsum($_) <=> $_ }

```

Output:

```
Bag(Less(15043), More(4953), Same(4))
```