We define the Perfect Number is a positive integer that is equal to the sum of all its positive divisors except itself.

Now, given an integer n, write a function that returns true when it is a perfect number and false when it is not.

 

Example:

Input: 28
Output: True
Explanation: 28 = 1 + 2 + 4 + 7 + 14

 

Note: The input number n will not exceed 100,000,000. (1e8)

 

题解如下：

class Solution {
    public boolean checkPerfectNumber(int num) {
        if(num <= 0) {
            return false;
        }
        int sum = 0;
        for(int i = 1;i * i <= num;i++) {
            if(num % i == 0) {
                sum += i;
                if(i * i != num) {
                    sum += num/i;
                }
            }
        }
        return sum - num == num;
    }
}

tips:如果一个数可以被一个数整除，那么与它对应的另一个除数也可以被被除数整除