Score : 300 points
Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.
Input is given from Standard Input in the following format:
K
Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.
2
9
\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2) +\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2) =1+1+1+1+1+1+1+2=9
Thus, the answer is 9.
200
10813692