{"raw_statement":[{"iden":"problem statement","content":"Find $\\displaystyle{\\sum_{a=1}^{K}\\sum_{b=1}^{K}\\sum_{c=1}^{K} \\gcd(a,b,c)}$.\nHere $\\gcd(a,b,c)$ denotes the greatest common divisor of $a$, $b$, and $c$."},{"iden":"constraints","content":"*   $1 \\leq K \\leq 200$\n*   $K$ is an integer."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$K$"},{"iden":"sample input 1","content":"2"},{"iden":"sample output 1","content":"9\n\n$\\gcd(1,1,1)+\\gcd(1,1,2)+\\gcd(1,2,1)+\\gcd(1,2,2)$ $+\\gcd(2,1,1)+\\gcd(2,1,2)+\\gcd(2,2,1)+\\gcd(2,2,2)$ $=1+1+1+1+1+1+1+2=9$\nThus, the answer is $9$."},{"iden":"sample input 2","content":"200"},{"iden":"sample output 2","content":"10813692"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}