GCDExtreme.java

/*Given the value of N, you will have to find the value of G. The meaning of G is given in the following code
G=0;
for(i = 1 ; i < N ; i++)
   for(j = i+1 ; j <= N ; j++) 
       G+=gcd(i,j);
Here gcd() is a function that finds the greatest common divisor of the two input numbers.
Input
The input file contains at most 20000 lines of inputs. Each line contains an integer N (1 < N < 1000001). The meaning of N is given in the problem statement. Input is terminated by a line containing a single zero.
Output
For each line of input produce one line of output. This line contains the value of G for the corresponding N. The value of G will fit in a 64-bit signed integer.
Sample Input:
10
100
200000
0
Sample Output:
67
13015
143295493160*/
import java.util.*;
import java.io.*;
public class GCDExtreme {
	static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
    static Reader sc = new Reader();
    static long phi[] = new long[1000001];
    static long sumj[] = new long[1000001];
    static long dp[] = new long[1000001];
    static int N = dp.length;
    static void processPhi(){
        for(int i=0;i<N;i++){phi[i] = i;}
        for(int i=2;i*2<N;i++){
            if(phi[i] == i){
				for(int j=i*2;j<N;j+=i){
					phi[j] *= i-1;
                    phi[j] /= i;
                }
            }
        }
        for(int i=1;i<N;i++){
			if(phi[i] == i){phi[i]--;}
        }
    }
    static void processSumJ(){
		for(int i=1;i*i<N;i++){
			for(int j=i*i;j<N;j+=i){
				sumj[j] += i*phi[j/i];
                if(i!=j/i){
                    sumj[j] += (j/i)*phi[i];
                }
            }
        }
    }
	static void preCompute(){
		processPhi();
        processSumJ();
        for(int i=1;i<N;i++){
			dp[i] = sumj[i] + dp[i-1];
        }
    }
	public static void main(String[] args)throws IOException {
		int n;
        preCompute();
         while((n=sc.nextInt())!=0){
			System.out.println(getSum(n));
        }
	}
    static long getSum(int n){
		return dp[n];
    }

}