sicily 1089 欧拉函数递推

//f[n] = f[n-1] + fai[n] //欧拉函数 质因子个数/n 包括本身//fai[n] = n * (1 - 1/a)*.... a为质因子#include <iostream>#include <cstring>#include <cmath>#define mx 1000010using namespace std;int prime[mx];bool isprime[mx];long long f[1000010]; //long long 贡献一次wadouble fai[1000010];void primeList(){memset( isprime,true,sizeof( isprime ) );for( int i = 2;i < mx;i++ ){if( isprime[i] ) prime[++prime[0]] = i;for( int j = 1; j <= prime[0] && i * prime[j] < mx;j++ ){isprime[i*prime[j]] = false;if( 0 == i % prime[j] ) break;}}}int main() {primeList();f[2] = 1;f[3] = 3;for( int i = 4;i <= 1000000;i++ ) fai[i] = i;for( int i = 2;i <= 1000000;i++ ) //一开始把 i<sqrt() 当然WA。。{if( isprime[i] ){for( int j = i;j <= 1000000;j += i ) // fai = fai * (1-1/a) *(1-1/b)*... a b 为其质因子{fai[j] = fai[j] / i * ( i - 1 );}}}for( int i = 4;i <= 1000000;i++ ){f[i] = f[i-1] + fai[i];}int n;while( cin>>n && n != 0) cout<<f[n]<<endl;return 0;}