101622: [AtCoder]ABC162 C - Sum of gcd of Tuples (Easy)

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:1 Solved:0

Description

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

Input

题意翻译

求 $$\sum_{a=1}^K\sum_{b=1}^K\sum_{c=1}^Kgcd(a,b,c)$$ 的值。

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