Problem:
Score : 300 points

Problem Statement

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.

Constraints

1 \leq K \leq 200

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.

Sample Input 1

2

Sample Output 1

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.

Sample Input 2

200

Sample Output 2

10813692

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class Progaram
{
    static void Main(string[] args)
    {
        var k = int.Parse(Console.ReadLine());
        long res = 0;
        Func<int, int, int> yug = (a, b) =>
        {
            int r = 201;
            while (true)
            {
                r = a % b;
                if (r == 0) break;
                a = b;
                b = r;
            }
            return b;
        };
        for (var al = 1; k >= al; al++)
        {
            for (var bl = 1; k >= bl; bl++)
            {
                for (var cl = 1; k >= cl; cl++)
                {
                    int a = al;
                    int b = bl;
                    int c = cl;
                    b = yug(a, b);
                    a = b;
                    b = c;
                    b = yug(a, b);
                    res += b;
                }
            }
        }
        Console.WriteLine(res);
    }
}