507. Perfect Number

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)

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所有得因子之和等于该数字的数被成为完美数。给定要给数字，判断其是否为完美数

乍看题目比较简单，就直接写呗

     public static boolean checkPerfectNumber(int num) {
            if(num == 1) return false;
            int sum = 0;
            for(int i = 1; i < num; i++)
                if(num % i == 0)
                    sum += i;
            return sum == num;
        }

可是提交了一下，发现超时，这时候就需要做一定的优化了。就像以前求素数的方法，对输入的数求平方根

    public boolean checkPerfectNumber(int num) {
        if(num == 1) return false;
        int sum = 1;
        for(int i = 2; i < Math.sqrt(num); i++)
            if(num % i == 0)
            {
                sum += i;
                sum += num/i;
            }

        return sum == num;
    }