2478Farey Sequence欧拉函数

Farey Sequence Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 7076 Accepted: 2610

Description

The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few are F2 = {1/2} F3 = {1/3, 1/2, 2/3} F4 = {1/4, 1/3, 1/2, 2/3, 3/4} F5 = {1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5} You task is to calculate the number of terms in the Farey sequence Fn.

Input

There are several test cases. Each test case has only one line, which contains a positive integer n (2 <= n <= 10 ⁶). There are no blank lines between cases. A line with a single 0 terminates the input.

Output

For each test case, you should output one line, which contains N(n) ---- the number of terms in the Farey sequence Fn.

Sample Input

2 3 4 5 0

Sample Output

1 3 5 9

Source

POJ Contest,Author:Mathematica@ZSU

 

#include<cstdio> #include<cstring> #include<iostream> using namespace std; //基于素数筛选法，计算欧拉函数phi[1] to phi[MAX],复杂度约为n，很快 //传入三个数组: //phi[]用于存放欧拉函数 //prime[]用来存放小于i的所有素数，这里其实是一个模拟堆栈 //isprime[]用来标志该数是不是素数，初始值为0 /* 这个算法的核心，基于以下这个定理： 若(N%a==0 && (N/a)%a==0) 则有:E(N)=E(N/a)*a; 若(N%a==0 && (N/a)%a!=0) 则有:E(N)=E(N/a)*(a-1); */ #define MAX 1000000 __int64 phi[MAX+1]={0}; __int64 prime[MAX+1]={0}; bool isprime[MAX+1]={0}; void get_phi()//这是一个基于素数筛选的线性算法，很快 { __int64 i,j; __int64 len=0; for(i=2;i<=MAX;i++) { if(isprime[i]==false) //false代表是质数 { prime[++len]=i; phi[i]=i-1; } for(j=1;j<=len&&prime[j]*i<=MAX;j++) { isprime[prime[j]*i]=true;//true代表是合数 if(i%prime[j]==0) { phi[i*prime[j]]=phi[i]*prime[j]; break; } else phi[i*prime[j]]=phi[i]*(prime[j]-1); } } } /**//END_TEMPLATE_BY_ABILITYTAO_ACM/// __int64 s[MAX]; int main() { __int64 i; phi[1]=0; get_phi(); for(i=2;i<=MAX;i++) s[i]=s[i-1]+phi[i]; while(1) { scanf("%I64d",&i); if(i==0) break; printf("%I64d/n",s[i]); } return 0; }