Perfect Numbers

You get an array of integers nums. Return the perfect numbers among them, in the same order.

A number is perfect when it equals the sum of its divisors smaller than itself. For example, 6 is perfect, because 1 + 2 + 3 = 6. The number 1 is not perfect. It has no smaller divisors, so its sum is 0.

If a perfect number appears twice, it is kept twice. If no number is perfect, the result is empty.

The work is split between two functions. The first one is a helper. It gets one number and returns the sum of its divisors smaller than itself. The second one is the function that is graded. It keeps every number that equals the sum the helper returns for it.

Example 1:

Input: nums = [6, 8, 28, 12]
Output: [6, 28]
Explanation: 6 = 1 + 2 + 3.
28 = 1 + 2 + 4 + 7 + 14.
For 8, the sum is 1 + 2 + 4 = 7.
For 12, the sum is 1 + 2 + 3 + 4 + 6 = 16.

Example 2:

Input: nums = [1, 5, 10]
Output: []
Explanation: The sum for 1 is 0.
The sum for 5 is 1.
The sum for 10 is 1 + 2 + 5 = 8.

Example 3:

Input: nums = [496, 6, 6]
Output: [496, 6, 6]
Explanation: 496 is perfect too.
6 appears twice, so it is kept twice.

Constraints:

• nums has 1 to 20 numbers.
• Every number is between 1 and 10,000.