{"problem":{"name":"Sum of gcd of Tuples (Easy)","description":{"content":"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 $c$.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc162_c"},"statements":[{"statement_type":"Markdown","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 $c$.\n\n## Constraints\n\n*   $1 \\leq K \\leq 200$\n*   $K$ is an integer.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc162_c","tags":[],"sample_group":[["2","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 $9$."],["200","10813692"]],"created_at":"2026-03-03 11:01:13"}}