{"id":374,"date":"2013-03-28T11:25:00","date_gmt":"2013-03-28T03:25:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/278"},"modified":"2013-03-28T11:25:00","modified_gmt":"2013-03-28T03:25:00","slug":"bzoj_2705_sdoi2012_problem_of_longge_-_euler_function_phi_i","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=374","title":{"rendered":"BZOJ 2705([SDOI2012]Longge\u7684\u95ee\u9898-\u6b27\u62c9\u51fd\u6570\u03c6(i))"},"content":{"rendered":"

<\/p>\n

2705: [SDOI2012]Longge\u7684\u95ee\u9898<\/h2>\n

Time Limit: <\/span>3 Sec  Memory Limit: <\/span>128 MB
\nSubmit: <\/span>375  Solved: <\/span>239
\n[Submit<\/a>][Status<\/a>][Discuss<\/a>]<\/center><\/p>\n

Description<\/h2>\n
\n
Longge\u7684\u6570\u5b66\u6210\u7ee9\u975e\u5e38\u597d\uff0c\u5e76\u4e14\u4ed6\u975e\u5e38\u4e50\u4e8e\u6311\u6218\u9ad8\u96be\u5ea6\u7684\u6570\u5b66\u95ee\u9898\u3002\u73b0\u5728\u95ee\u9898\u6765\u4e86\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570N\uff0c\u4f60\u9700\u8981\u6c42\u51fa\u2211gcd(i, N)(1<=i <=N)\u3002<\/span><\/div>\n<\/div>\n

Input<\/h2>\n
\n
\u4e00\u4e2a\u6574\u6570\uff0c\u4e3aN\u3002<\/span><\/div>\n<\/div>\n

Output<\/h2>\n
\n
\u4e00\u4e2a\u6574\u6570\uff0c\u4e3a\u6240\u6c42\u7684\u7b54\u6848\u3002<\/span><\/div>\n<\/div>\n

Sample Input<\/h2>\n
\n6

\n<\/span><\/div>\n

Sample Output<\/h2>\n
\n15

\n<\/span><\/div>\n

HINT<\/h2>\n
\n

\u3010\u6570\u636e\u8303\u56f4\u3011<\/p>\n

\u5bf9\u4e8e60%\u7684\u6570\u636e\uff0c0<N<=2^16\u3002<\/p>\n

\u5bf9\u4e8e100%\u7684\u6570\u636e\uff0c0<N<=2^32\u3002<\/p>\n

 <\/p>\n<\/p>\n<\/div>\n

\n<\/p>\n

\n<\/p>\n

\u6b27\u62c9\u51fd\u6570<\/a>\uff1a<\/span><\/p>\n<\/p>\n

\n\u679a\u4e3en\u7684\u7ea6\u6570k\uff0c\u4ee4s(k)\u4e3a\u6ee1\u8db3gcd(m,n)=k,(1<=m<=n)  m\u7684\u4e2a\u6570\uff0c\u5219ans=sigma(k*s(k)) (k\u4e3an\u7684\u7ea6\u6570\uff09<\/span><\/p>\n

\n \u56e0\u4e3agcd(m,n)=k,\u6240\u4ee5gcd(m\/k,n\/k)=1,\u4e8e\u662fs(k)=euler(n\/k)<\/span><\/p>\n

\n \u679a\u4e3en\u7684\u7ea6\u6570\u5373\u53ef\uff0c\u590d\u6742\u5ea6o(sqrt(n))<\/span><\/p>\n

PS:\u521a\u521aksy\u544a\u8bc9\u6211C++\uff0c\u76f4\u63a5\u8bfbint\u6bd4\u8bfbchar\u8f6cint\u6162\uff08\u2014\u20140\uff09<\/span><\/p>\n


\n<\/span><\/p>\n


\n<\/span><\/p>\n

<\/span><\/p>\n

#include<cstdio>\n#include<cstring>\n#include<cstdlib>\n#include<cmath>\n#include<functional>\n#include<algorithm>\n#include<cctype>\n#include<iostream>\nusing namespace std;\n#define MAXN (2<<31)\nlong long ans=0,n;\nlong long phi(long long n)\n{\n\tif (n==1) return 1;\n\/\/\tcout<<n;\n\tlong long ans=1;\n\tfor (long long i=2;i*i<=n;i++)\n\t\tif (n%i==0)\n\t\t{\n\t\t\tint k=0;\n\t\t\twhile (n%i==0) {k++,n\/=i;}\n\t\t\tans*=i-1;\n\t\t\tfor (int j=2;j<=k;j++) ans*=i;\n\t\t}\n\tif (n>1) ans*=n-1;\n\/\/\tcout<<' '<<ans<<endl;\n\treturn ans;\n}\nint main()\n{\n\tcin>>n;\n\tfor (int i=1;i*i<=n;i++)\n\t\tif (n%i==0)\n\t\t{\n\t\t\tans+=(long long)i*phi(n\/i);\n\t\t\tif (i*i<n) ans+=(long long)n\/i*phi(i);\n\t\t}\n\tcout<<ans<<endl;\n\treturn 0;\n}<\/pre><\/p>\n","protected":false},"excerpt":{"rendered":"
2705: [SDOI2012]Longge\u7684\u95ee\u9898 Time Limit: 3 Sec & […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[3],"tags":[100],"class_list":["post-374","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-euler_function"],"yoast_head":"\nBZOJ 2705([SDOI2012]Longge\u7684\u95ee\u9898-\u6b27\u62c9\u51fd\u6570\u03c6(i)) - nike0good<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nike0good.com\/?p=374\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"BZOJ 2705([SDOI2012]Longge\u7684\u95ee\u9898-\u6b27\u62c9\u51fd\u6570\u03c6(i)) - 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