{"problem":{"name":"[JRKSJ R6] 牵连的世界","description":{"content":"给定 $n,m$，求 $$\\sum_{i=1}^n \\sum_{j=1}^m \\sigma_0(ij)\\varphi(ij)$$","description_type":"Markdown"},"platform":"Luogu","limit":{"time_limit":1700,"memory_limit":262144},"difficulty":{"LuoguStyle":"P7"},"is_remote":true,"is_sync":true,"sync_url":null,"sign":"LGP8570"},"statements":[{"statement_type":"Markdown","content":"给定 $n,m$，求\n\n$$\\sum_{i=1}^n \\sum_{j=1}^m \\sigma_0(ij)\\varphi(ij)$$\n\n## Input\n\n两个整数 $n,m$。\n\n## Output\n\n一个整数，表示答案。答案对 $10^9+7$ 取模。\n\n[samples]\n\n## Background\n\n![](https://cdn.luogu.com.cn/upload/image_hosting/jdi9nrec.png)\n\n## Note\n\n$\\sigma_0,\\varphi$ 分别为因数个数函数，欧拉函数。\n\n本题可能轻微卡常。\n\n### 数据规模\n本题采用捆绑测试。\n\n| $\\text{Subtask}$ | $n,m\\le$ |  $\\text{Score}$ |\n| :----------: | :----------: | :----------: |\n| $1$ | $10^3$ | $10$ |\n| $2$ | $10^5$ |  $30$ |\n| $3$ | $2\\times 10^5$ | $30$ |\n| $4$ | $5\\times 10^5$ | $30$ |\n| $5$ | $3\\times 10^6$ | $1$ |\n\n对于所有数据，$1\\le n,m\\le 3\\times 10^6$。\n\n出于某些原因，你只要得到了 $\\ge 100$ 分就可以通过此题。","is_translate":false,"language":"English"}],"meta":{"iden":"LGP8570","tags":["2022","洛谷原创","O2优化","素数判断,质数,筛法","莫比乌斯反演"],"sample_group":[["5 5","453"],["20 20","173825"]],"created_at":"2026-03-03 11:09:25"}}