{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e一天,小Y遇到了一个让她困惑的函数。\u003c/p\u003e\u003cp\u003e$$$$$$ f(n) \u003d \\begin{cases} 1, \u0026amp; n \\in \\{1\\} \\bigcup \\operatorname{Prime} \\\\ p\\,f(p^{k-2}), \u0026amp; n \u003d p^k ~ (p \\in \\operatorname{Prime}; ~ k \u0026gt; 1) \\\\ f(p_1^{e_1})\\prod_{i\u003d2}^r {p_i}^{e_i}, \u0026amp; n \u003d \\prod_{i\u003d1}^r {p_i} ^ {e_i} ~ (p_1 \u0026lt; p_2 \u0026lt; \\cdots \u0026lt; p_r; ~ p_i \\in \\operatorname{Prime}; ~ r \\ge 2) \\end{cases} $$$$$$\u003c/p\u003e\u003cp\u003e现在小Y对$$$\\sum_{i\u003d1}^n f(i)$$$很感兴趣。你能帮帮她吗?\u003c/p\u003e"}},{"title":"输入","value":{"format":"HTML","content":"\u003cp\u003e一行,包含一个整数,表示$$$n ~ (1 \\le n \\le {10}^{7})$$$。\u003c/p\u003e"}},{"title":"输出","value":{"format":"HTML","content":"\u003cp\u003e一行,包含一个数字,表示答案。\u003c/p\u003e"}},{"title":"示例","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e10\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e20\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e100\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1487\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e"}},{"title":"注意","value":{"format":"HTML","content":"\u003cp\u003e对于第一个示例,$$$f(1) \u003d 1$$$,$$$f(2) \u003d 1$$$,$$$f(3) \u003d 1$$$,$$$f(4) \u003d 2$$$,$$$f(5) \u003d 1$$$,$$$f(6) \u003d 3$$$,$$$f(7) \u003d 1$$$,$$$f(8) \u003d 2$$$,$$$f(9) \u003d 3$$$,$$$f(10) \u003d 5$$$。\u003c/p\u003e\u003cp\u003e保证答案始终小于$$$2^{64}-1$$$。\u003c/p\u003e\u003cp\u003e小Y想知道你是否能解决$$$n$$$直到$$${10}^{10}$$$。\u003c/p\u003e"}}]}