HDOJ 2053 Switch Game

Problem Description
There are many lamps in a line. All of them are off at first. A series of operations are carried out on these lamps. On the i-th operation, the lamps whose numbers are the multiple of i change the condition ( on to off and off to on ).

Input
Each test case contains only a number n ( 0< n<= 10^5) in a line.

Output
Output the condition of the n-th lamp after infinity operations ( 0 - off, 1 - on ).

Sample Input
1
5

Sample Output
1
0

Hint
hint

Consider the second test case:

The initial condition : 0 0 0 0 0 …
After the first operation : 1 1 1 1 1 …
After the second operation : 1 0 1 0 1 …
After the third operation : 1 0 0 0 1 …
After the fourth operation : 1 0 0 1 1 …
After the fifth operation : 1 0 0 1 0 …

The later operations cannot change the condition of the fifth lamp any more. So the answer is 0.

The initial condition : 0 0 0 0 0 …
After the first operation : 1 1 1 1 1 …
After the second operation : 1 0 1 0 1 …
After the third operation : 1 0 0 0 1 …
After the fourth operation : 1 0 0 1 1 …
After the fifth operation : 1 0 0 1 0 …
这是一个例子，分析这个例子，你可以推断出题目的意思。暴力达标的话会超时，因为要用两层10^5，

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        while(sc.hasNext()){
            int n=sc.nextInt();
            int k=0;
            for(int i=1;i<=n;i++){
                if(n%i==0){
                    k=1-k;
                }
            }
            System.out.println(k);
        }
    }

}