hdu1787 GCD Again poj 2478 Farey Sequence 欧拉函数

hdu1787，直接求欧拉函数

#include <iostream>
#include <cstdio>
using namespace std;
int n;
int phi(int n){
	int ans=n;
	for(int i=2; i*i<=n; i++)
		if(n%i==0){
			ans -= ans / i;
			while(n%i==0)	n /= i;
		}
	if(n>1)	ans -= ans / n;
	return ans;
}
int main(){
	while(scanf("%d", &n)!=EOF){
		if(!n)	break;
		printf("%d\n",n-phi(n)-1);
	}
	return 0;
}

poj2478，欧拉函数递推，证明可以看这里或者是算法竞赛进阶指南

\(n \log n\) 筛

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
int n;
long long phi[1000005];
void shai(){
	for(int i=2; i<=1000000; i++)
		phi[i] = i;
	for(int i=2; i<=1000000; i++)
		if(phi[i]==i)
			for(int j=i; j<=1000000; j+=i)
				phi[j] = phi[j] / i * (i - 1);
}
int main(){
	shai();
	for(int i=2; i<=1000000; i++)
		phi[i] += phi[i-1];
	while(scanf("%d", &n)!=EOF){
		if(!n)	break;
		printf("%lld\n", phi[n]);
	}
	return 0;
}

线性筛：

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
typedef long long ll;
int n, pri[1000005], cnt;
ll phi[1000005];
bool isp[1000005];
void shai(){
	memset(isp, true, sizeof(isp));
	isp[0] = isp[1] = false;
	for(int i=2; i<=1000000; i++){
		if(isp[i])	pri[++cnt] = i, phi[i] = i - 1;
		for(int j=1; j<=cnt; j++){
			if(i*pri[j]>1000000)	break;
			isp[i*pri[j]] = false;
			if(i%pri[j]==0){
				phi[i*pri[j]] = phi[i] * pri[j];//感性理解：12：1 5 7 11
				break;
			}
			else	phi[i*pri[j]] = phi[i] * (pri[j] - 1);//积性函数
		}
	}
}
int main(){
	shai();
	for(int i=2; i<=1000000; i++)
		phi[i] += phi[i-1];
	while(scanf("%d", &n)!=EOF){
		if(!n)	break;
		printf("%lld\n", phi[n]);
	}
	return 0;
}

上面那种得到了素数，下面这种得到了最小质因子

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
int n, pri[1000005], cnt, val[1000005];
long long phi[1000005];
void shai(){
	for(int i=2; i<=1000000; i++){
		if(!val[i]){
			val[i] = i;
			pri[++cnt] = i;
			phi[i] = i - 1;
		}
		for(int j=1; j<=cnt; j++){
			if(pri[j]>val[i] || pri[j]>1000000/i)	break;
			val[i*pri[j]] = pri[j];
			phi[i*pri[j]] = phi[i]*(i%pri[j]?(pri[j]-1):pri[j]);
		}
	}
}
int main(){
	shai();
	for(int i=2; i<=1000000; i++)
		phi[i] += phi[i-1];
	while(scanf("%d", &n)!=EOF){
		if(!n)	break;
		printf("%lld\n", phi[n]);
	}
	return 0;
}