{"categories":["\u6574\u6570\u8ad6","\u7d20\u6570","\u7d20\u6570\u5b9a\u7406","Euler \u306e totient \u95a2\u6570"],"blog_url":"https://info.atcoder.jp/","provider_url":"https://hatena.blog","author_url":"https://blog.hatena.ne.jp/atcoder/","url":"https://info.atcoder.jp/entry/algorithm_lectures/prime_related_complexity","version":"1.0","author_name":"atcoder","published":"2026-04-10 14:10:58","height":"190","title":"\u7d20\u6570\u306b\u95a2\u3059\u308b\u8a55\u4fa1","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Finfo.atcoder.jp%2Fentry%2Falgorithm_lectures%2Fprime_related_complexity\" title=\"\u7d20\u6570\u306b\u95a2\u3059\u308b\u8a55\u4fa1 - AtCoderInfo\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","type":"rich","image_url":"https://cdn.user.blog.st-hatena.com/default_entry_og_image/158934417/1702097020779738","width":"100%","description":"\u89e3\u8aac\u52d5\u753b\u306f\u3053\u3061\u3089\u3067\u3059\uff0e 1. \u6982\u8981 \u7af6\u6280\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u5b66\u7fd2\u3092\u3057\u3066\u3044\u308b\u3068\uff0c\u6b21\u306e\u3088\u3046\u306a\u7d50\u679c\u3092\u76ee\u306b\u3059\u308b\u3053\u3068\u304c\u3042\u308b\u3068\u601d\u3044\u307e\u3059\uff0e $N$ \u4ee5\u4e0b\u306e\u7d20\u6570\u306e\u500b\u6570\u306f $\\displaystyle \\frac{N}{\\log N}$ \u7a0b\u5ea6\u3067\u3042\u308b\uff08\u7d20\u6570\u5b9a\u7406\uff09\uff0e $N$ \u4ee5\u4e0b\u306e\u7d20\u6570\u306e\u9006\u6570\u306e\u7dcf\u548c $\\displaystyle \\sum_{p\\leq N}\\frac{1}{p}$ \u306f $\\log\\log N$ \u7a0b\u5ea6\u3067\u3042\u308b\uff08Mertens \u306e\u5b9a\u7406\uff09\uff0e \u306a\u304a\uff0c\u672c\u8a18\u4e8b\u3067\u306f $p$ \u3068\u66f8\u3051\u3070\u7d20\u6570\u3092\u8868\u3059\u3082\u306e\u3068\u3057\uff0c$N$ \u4ee5\u4e0b\u306e\u7d20\u6570\u306b\u5bfe\u3059\u308b\u548c\u3092 $\\displaystyle \\sum _ {p\\leq N} \\frac{1}{p}\u2026","provider_name":"Hatena Blog","blog_title":"AtCoderInfo"}