---
id: 594810f028c0303b75339acd
title: 'Abundant, deficient and perfect number classifications'
challengeType: 5
forumTopicId: 302221
dashedName: abundant-deficient-and-perfect-number-classifications
---

# --description--

These define three classifications of positive integers based on their [proper divisors](<https://rosettacode.org/wiki/Proper divisors> "Proper divisors").

Let $P(n)$ be the sum of the proper divisors of `n` where proper divisors are all positive integers `n` other than `n` itself.

If `P(n) < n` then `n` is classed as `deficient`

If `P(n) === n` then `n` is classed as `perfect`

If `P(n) > n` then `n` is classed as `abundant`

**Example**: `6` has proper divisors of `1`, `2`, and `3`. `1 + 2 + 3 = 6`, so `6` is classed as a perfect number.

# --instructions--

Implement a function that calculates how many of the integers from `1` to `20,000` (inclusive) are in each of the three classes. Output the result as an array in the following format `[deficient, perfect, abundant]`.

# --hints--

`getDPA` should be a function.

```js
assert(typeof getDPA === 'function');
```

`getDPA` should return an array.

```js
assert(Array.isArray(getDPA(100)));
```

`getDPA` return value should have a length of 3.

```js
assert(getDPA(100).length === 3);
```

`getDPA(20000)` should equal [15043, 4, 4953]

```js
assert.deepEqual(getDPA(20000), solution);
```

# --seed--

## --after-user-code--

```js
const solution = [15043, 4, 4953];
```

## --seed-contents--

```js
function getDPA(num) {

}
```

# --solutions--

```js
function getDPA(num) {
  const dpa = [1, 0, 0];
  for (let n = 2; n <= num; n += 1) {
    let ds = 1;
    const e = Math.sqrt(n);
    for (let d = 2; d < e; d += 1) {
      if (n % d === 0) {
        ds += d + (n / d);
      }
    }
    if (n % e === 0) {
      ds += e;
    }
    dpa[ds < n ? 0 : ds === n ? 1 : 2] += 1;
  }
  return dpa;
}
```