507. Perfect Number

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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:

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

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

解法1：

每一个divisor都有对应的另外一个divisor， 每次找到一个小的divisor之后对应的大的divisor就成为了新的边界，因为不会再出现比大的divisor再大的没遇见的divisor。
C++

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Java

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public class Solution {
    public boolean checkPerfectNumber(int num) {
        int sum = 1;
        int i = 2;
        int right = num;
        while ( i < right) {
            if (num % i == 0) {
                sum += i;
                sum += (num / i);   // the other side,
            }
            right = num / i;
            i++;
        }
        return sum == num && num != 1;
    }
}