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;

public class ABC162C {
	private static void Main(string[] args) {
		var k = ReadInt();
		var answer = 0;

		for (int a = 1; a <= k; a++)
			for (int b = 1; b <= k; b++)
				for (int c = 1; c <= k; c++)
					answer += CalcGCD(a, b, c);

		Console.WriteLine(answer);
	}

	private static int ReadInt() => int.Parse(Console.ReadLine().Trim());
	private static int GCD(int a, int b) => b == 0 ? a : GCD(b, a % b);
	private static int CalcGCD(int a, int b) => a > b ? GCD(a, b) : GCD(b, a);
	private static int CalcGCD(int a, int b, int c) => CalcGCD(CalcGCD(a, b), c);
}