思路
求和+求公约数。什么时候做困难题也能像做简单题这么轻松就好了~ 
代码
class Solution {
    public int gcdOfOddEvenSums(int n) {
        int sumOdd = (1 + 2 * n - 1) * n / 2;
        int sumEven = (2 + 2 * n) * n / 2;
        return gcd(sumOdd, sumEven);
    }
    private int gcd(int a, int b) {
        while (b != 0) {
            int temp = a;
            a = b;
            b = temp % b;
        }
        return a;
    }
}