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 Scala (2.13.1) (judge verdict: Accepted)

import java.util.Scanner


object Main {
  def main(args: Array[String]): Unit = {
    val sc = new Scanner(System.in)
    val k = sc.nextInt()
    var ans: Long = 0L
    
    for (i <- 1 to k) {
      for (j <- 1 to k) {
        for (n <- 1 to k) {
          ans += gcds(i, j, n)
        }
      }
    }
    
    println(ans)
  }
  
  def gcds(a: Int, b: Int, c: Int): Int = {
    val m = gcd(a, b)
    gcd(m, c)
  }
  
  def gcd(a: Int, b: Int): Int = {
    if (a % b == 0) {
      b
    } else {
      gcd(b, a % b)
    }
  }
  
  def printArray[T](arr: Array[T]): Unit = {
    for (i <- arr.indices) {
      print(s"${arr(i)} ")
    }
    println()
  }
}