507. Perfect Number

1. Description

A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. A divisor of an integer x is an integer that can divide x evenly.
Given an integer n, return true if n is a perfect number, otherwise return false.

2. Example

Example 1

Input: num = 28
Output: true
Explanation: 28 = 1 + 2 + 4 + 7 + 14
1, 2, 4, 7, and 14 are all divisors of 28.

Example 2

Input: num = 6
Output: true

Example 3

Input: num = 496
Output: true

Example 4

Input: num = 8128
Output: true

Example 5

Input: num = 2
Output: false

3. Constraints

• 1 <= num <= 10$^{8}$

4. Solutions

Math

n = number
Time complexity: O($\sqrt{n}$)
Space complexity: O(1)

class Solution
{
public:
    // bool checkPerfectNumber(int num)
    bool checkPerfectNumber(int number)
    {
        int sum = 0;
        for(int i = 1; i * i <= number; i++)
        {
            if(number % i == 0)
            {
                sum += i;

                if(i * i != number)
                    sum += (number / i);
            }
        }

        // we start from 1, so it will include the number itself
        return (sum == number * 2);
    }
};