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 kotlin.math.min

fun main(args:Array<String>){
    val k = readLine()!!.toInt()
    var result = 0
    for(a in 1..k){
        for(b in 1..k){
            for(c in 1..k){
                val m = min(a,min(b,c))
                var sum = 0
                var start = 1
                if(a%2==0&&b%2==0&&c%2==0){
                    start *= 2
                }
                if(a%3==0&&b%3==0&&c%3==0){
                    start *= 3
                }
                if(a%5==0&&b%5==0&&c%5==0){
                    start *= 5
                }
                if(a%7==0&&b%7==0&&c%7==0){
                    start *= 7
                }
                for(i in start..m step start){
                    if(a%i==0&&b%i==0&&c%i==0){
                        sum =i
                    }
                }
                result += sum
            }
        }
    }
    println(result)
}