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## Page 1

11417
GCD
Given the value of N, you will have to find the value of G. The definition of G is given below:
G =
i<N

∑

i=1

j≤N

∑

j=i+1

GCD(i, j)

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 100 lines of inputs. Each line contains an integer N (1 < N < 501).

The meaning of N is given in the problem statement. Input is terminated by a line containing a single

zero. This zero should not be processed.

Output

For each line of input produce one line of output. This line contains the value of G for corresponding

N.

Sample Input

10

100

500

0

Sample Output

67

13015

442011