http://poj.org/problem?id=3090

法雷級數

法雷級數的遞推公式非常easy：f[1] = 2; f[i] = f[i-1]+phi[i]。

該題是法雷級數的變形吧，答案是2*f[i]-1。

#include <stdio.h> #include <iostream> #include <map> #include <set> #include <stack> #include <vector> #include <math.h> #include <string.h> #include <queue> #include <string> #include <stdlib.h> #include <algorithm> #define LL long long #define _LL __int64 #define eps 1e-12 #define PI acos(-1.0) using namespace std;const int maxn = 1100;int flag[maxn]; int prime[maxn]; int phi[maxn]; LL f[maxn];void init() {memset(flag,0,sizeof(flag));prime[0] = 0;phi[1] = 1;for(int i = 2; i < maxn; i++){if(flag[i] == 0){phi[i] = i-1;prime[++prime[0]] = i;}for(int j = 1; j <= prime[0]&&prime[j]*i<maxn; j++){flag[prime[j]*i] = 1;if(i % prime[j] == 0)phi[prime[j]*i] = phi[i] * prime[j];elsephi[prime[j]*i] = phi[i] * (prime[j] - 1);}}f[1] = 2;for(int i = 2; i <= 1000; i++)f[i] = f[i-1] + phi[i]; }int main() {init();int test;scanf("%d",&test);for(int item = 1; item <= test; item++){int x;scanf("%d",&x);printf("%d %d %lld\n",item,x,f[x]*2-1);}return 0; }

http://poj.org/problem?

id=2478

更簡單了，直接求法雷級數?；谒財岛Y的歐拉函數。

#include <stdio.h> #include <iostream> #include <map> #include <set> #include <stack> #include <vector> #include <math.h> #include <string.h> #include <queue> #include <string> #include <stdlib.h> #include <algorithm> #define LL long long #define _LL __int64 #define eps 1e-12 #define PI acos(-1.0) using namespace std;const int maxn = 1000010;int flag[maxn]; int prime[maxn]; int phi[maxn]; LL f[maxn];void init() {memset(flag,0,sizeof(flag));prime[0] = 0;phi[1] = 1;for(int i = 2; i < maxn; i++){if(flag[i] == 0){phi[i] = i-1;prime[++prime[0]] = i;}for(int j = 1; j <= prime[0]&&prime[j]*i<maxn; j++){flag[prime[j]*i] = 1;if(i % prime[j] == 0)phi[prime[j]*i] = phi[i] * prime[j];elsephi[prime[j]*i] = phi[i] * (prime[j] - 1);}}f[1] = 2;for(int i = 2; i <= 1000010; i++)f[i] = f[i-1] + phi[i]; }int main() {init();int n;while(~scanf("%d",&n)&&n){printf("%lld\n",f[n]-2);}return 0; }

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