杜教筛入门

https://www.51nod.com/onlineJudge/questionCode.html#!problemId=1239

51nod 1239

欧拉函数之和

#include<cstdio>
#include<map>
const int N=10000011,maxn=10000000;
const int mod=1e9+7;
typedef long long ll;
std::map<ll,ll>mp;
int pr[N];
bool ip[N];
int phi[N];
int sum[N];
inline void shai_fa(){
	phi[1]=1ll;
	for(register int i=2;i<=maxn;++i){
		if(!ip[i])
			phi[pr[++pr[0]]=i]=i-1;
		for(register int j=1;j<=pr[0]&&pr[j]*i<=maxn;++j){
			ip[i*pr[j]]=1;
			if(i%pr[j]==0){
				phi[i*pr[j]]=pr[j]*phi[i];
				break;
			}
			phi[i*pr[j]]=phi[i]*phi[pr[j]];
		}
	}
	for(register int i=1;i<=maxn;++i)
		sum[i]=(sum[i-1]+phi[i])%mod;
}
ll T,n;
inline ll query(ll x){
	if(x<=maxn)return sum[x];
	if(mp[x])return mp[x];
	ll ans=1ll*x%mod*(x%mod+1)/2;
	ll pos;
	for(register ll i=2;i<=x;i=pos+1){
		pos=x/(x/i);
		ans-=1ll*(pos-i+1)*query(x/i)%mod;
		ans=(ans+mod)%mod;
	}
	return mp[x]=ans;
}
int main(){
	shai_fa();
	scanf("%lld",&n);
	printf("%lld
",query(n));
	return 0;
}

　　

https://www.51nod.com/onlineJudge/questionCode.html#!problemId=1244

51nod 1244

莫比乌斯函数之和

#include<cstdio>
#include<map>
const int N=10000011,maxn=10000000;
const int mod=1e9+7;
typedef long long ll;
std::map<ll,ll>mp;
std::map<ll,bool>vis;
int pr[N];
bool ip[N];
int miu[N];
inline void shai_fa(){
	miu[1]=1;
	for(register int i=2;i<=maxn;++i){
		if(!ip[i])
			miu[pr[++pr[0]]=i]=-1;
		for(register int j=1;j<=pr[0]&&pr[j]*i<=maxn;++j){
			ip[i*pr[j]]=1;
			if(i%pr[j]==0)
				break;
			miu[i*pr[j]]=-miu[i];
		}
	}
	for(register int i=1;i<=maxn;++i)
		miu[i]=(miu[i-1]+miu[i])%mod;
}
ll a,b;
inline ll query(ll x){
	if(x<=maxn)return miu[x];
	if(vis[x])return mp[x];
	ll ans=1,pos;
	for(ll i=2;i<=x;i=pos+1){
		pos=x/(x/i);
		ans-=1ll*(pos-i+1)*query(x/i);
	}
	vis[x]=1;
	return mp[x]=ans;
}
int main(){
	shai_fa();
	scanf("%lld%lld",&a,&b);
	printf("%lld
",query(b)-query(a-1));
	return 0;
}