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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.util.Scanner

fun main(args: Array<String>) {
	val scn = Scanner(System.`in`)
	val k = scn.nextInt()
	var sum = 0L
	for (a in 1..k){
		for(b in a..k){
			val ab = gcd(b, a)
			for (c in b..k){
				val t = when{
					a==c -> 1
					a==b || b==c -> 3
					else -> 6
				}
				sum += t*gcd(ab, c)
			}
		}
	}
	println(sum)
}

fun gcd(a: Int, b: Int): Int{
	var a = a; var b = b
	if (a<b) {
		val tmp = a; a = b; b = tmp
	}
	if (a%b==0) return b
	else return gcd(b, a%b)
}