GCD Extreme (I)

Given the value of N, you will have to find the value of G. The definition of G is given below: i<N j≤N ∑∑ G= GCD(i,j) i=1 j=i+1 Here GCD(i,j) means the greatest common divisor of integer i and integer j. For those who have trouble understanding summation notation, 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 < 200001). 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 20000 0 Sample Output 67 13015 1153104356