[歐拉函數]HDU 2824 The Euler function 題解

題目大意

求$\sum_{i=L}^R \varphi(i)$

解題分析

水題，前綴和構造，注意空間不要爆

示例代碼

題目傳送門

#include<cstdio>
using namespace std;
typedef long long LL;
const int maxn=3000005;
int s,t,p[maxn];
bool vs[maxn];
LL phi[maxn];
void makep(){
	vs[0]=vs[1]=0; p[0]=0; phi[1]=1;
	for (int i=2;i<=3e6;i++){
		if (!vs[i]) {p[++p[0]]=i; phi[i]=i-1;}
		for (int j=1;j<=p[0]&&i*p[j]<=3e6;j++){
			vs[i*p[j]]=1;
			if (i%p[j]) phi[i*p[j]]=phi[i]*phi[p[j]];
			else {phi[i*p[j]]=phi[i]*p[j]; break;}
		}
	}
	for (int i=2;i<=3e6;i++) phi[i]+=phi[i-1];
}
int main()
{
	freopen("euler.in","r",stdin);
	freopen("euler.out","w",stdout);
	makep();
	while (scanf("%d%d",&s,&t)==2) printf("%lld\n",phi[t]-phi[s-1]);
	return 0;
}