A perfect number is a positive integer that is equal to the sum of its proper divisors (divisors excluding the number itself).

Your task is to create a method that checks if a given number is a perfect number.

A proper divisor of a number is any divisor except the number itself. For example, the proper divisors of 6 are 1, 2, and 3.

The method should:

  • Return true if the number is a perfect number
  • Return false if the number is not a perfect number
  • Return false for numbers less than or equal to 1
  • Return null for null input

Examples

Example 1:

Input: 6 Output: true Explanation: The proper divisors of 6 are 1, 2, and 3. Their sum is 1 + 2 + 3 = 6

Example 2:

Input: 28 Output: true Explanation: The proper divisors of 28 are 1, 2, 4, 7, and 14. Their sum is 1 + 2 + 4 + 7 + 14 = 28

Example 3:

Input: 12 Output: false Explanation: The proper divisors of 12 are 1, 2, 3, 4, and 6. Their sum is 1 + 2 + 3 + 4 + 6 = 16, which is not equal to 12

Example 4:

Input: 1 Output: false Explanation: 1 has no proper divisors, so it is not a perfect number

Example 5:

Input: null Output: null Explanation: Null input returns null
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