51nod 237 最大公约数之和 V3 杜教筛

Code:

#include <bits/stdc++.h>
#include <tr1/unordered_map>

#define setIO(s) freopen(s".in","r",stdin)
#define ll long long
#define ull unsigned long long
#define maxn 10000000
#define mod 1000000007
#define inv 500000004

using namespace std;
using namespace tr1;
int vis[maxn],prime[maxn],tot;
ll phi[maxn];
unordered_map<ll,ull>ansphi;
void init(){
    phi[1] = 1;
    for(int i=2;i<maxn; ++i) {
        if(!vis[i]) prime[++tot]=i,phi[i] = i-1;
        for(int j=1;j<=tot&&i*prime[j]<maxn;++j) {
            vis[i*prime[j]]=1;
            if(i%prime[j]!=0) phi[i*prime[j]]=phi[i]*(prime[j]-1);
            else {
                phi[i*prime[j]]=phi[i]*(prime[j]);
                break;
            }
        }
    }
    for(int i=1;i<maxn;++i) phi[i]+=phi[i-1],phi[i]%=mod;
}
ll solve(ll n){
    if(n < maxn) return phi[n];
    if(ansphi[n]) return ansphi[n];
    ll ans=(ull)(((n%mod)*((n+1)%mod) %mod)*(inv%mod))%mod;
    ll ans2=0;
    for(ll l=2,r;l<=n;l=r+1) {
        r=n/(n/l);
        ans2+=(ll)(r-l+1)*solve(n/l);
        ans2%=mod;
    }
    return ansphi[n]=(ans+mod-ans2)%mod;
}
int main(){
    //setIO("input");
    init();
    ll n,ans=0,ans1,tmp;
    scanf("%lld",&n);
    for(ll l=1,r;l<=n;l=r+1){
        r=(n/(n/l));
        ans+=(((n/l)%mod)*((n/l)%mod)%mod*(solve(r)+mod-solve(l-1))%mod)%mod;
        ans%=mod;
    }
    printf("%lld",ans);
    return 0;
}