题目链接
一定要记得随时取模和%mmh学长。
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<string>
#include<queue>
#include<map>
#include<unordered_map>
#define ll long long
#define llu unsigned ll
using namespace std;
const int maxn=200100;
const int mod=1e9+7;
ll p[maxn],id1[maxn],id2[maxn];
ll g[maxn],h[maxn],sum[maxn],sum2[maxn],wi[maxn];
int cnt;
bool ha[maxn];
ll n,inv2,inv6,sq;
ll mypow(ll a,ll b)
{
ll ans=1;
while(b)
{
if(b&1) ans=ans*a%mod;
a=a*a%mod;
b>>=1;
}
return ans;
}
void Prime(ll n)
{
ha[1]=true;
for(int i=2;i<=n;i++)
{
if(!ha[i])
{
p[++cnt]=i;
sum[cnt]=(sum[cnt-1]+i)%mod;
sum2[cnt]=(sum2[cnt-1]+1ll*i*i)%mod;
}
for(int j=1;j<=cnt&&p[j]*i<=n;j++)
{
ha[i*p[j]]=true;
if(i%p[j]==0) break;
}
}
}
int getid(ll m)
{
if(m<=sq) return id1[m];
else return id2[n/m];
}
ll s(ll n,ll j)
{
if(n<=1||p[j]>n) return 0;
int k=getid(n);
ll res=(((g[k]-sum2[j-1])-(h[k]-sum[j-1]))%mod+mod)%mod;
for(int i=j;i<=cnt&&p[i]*p[i]<=n;i++)
{
ll p1=p[i],p2=p[i]*p[i];
for(int e=1;p2<=n;e++,p1=p2,p2=p2*p[i])
{
res=(res+s(n/p1,i+1)*(p1%mod)%mod*((p1-1)%mod)%mod+p2%mod*((p2-1)%mod)%mod)%mod;
}
}
return res;
}
ll getans1(ll n)
{
n%=mod;
return (n*(n+1)%mod*(2*n+1)%mod*inv6%mod-1+mod)%mod;
}
ll getans2(ll n)
{
n%=mod;
return (n*(n+1)%mod*inv2%mod-1+mod)%mod;
}
int main(void)
{
inv2=mypow(2,mod-2);
inv6=mypow(6,mod-2);
scanf("%lld",&n);
sq=sqrt(n*1.0);
Prime(sq);
int tot=0;
for(ll l=1,r;l<=n;l=r+1)
{
r=n/(n/l);
wi[++tot]=n/l;
if(wi[tot]<=sq) id1[wi[tot]]=tot;
else id2[n/wi[tot]]=tot;
g[tot]=getans1(wi[tot]);
h[tot]=getans2(wi[tot]);
}
for(int j=1;j<=cnt;j++)
{
for(int i=1;i<=tot&&p[j]*p[j]<=wi[i];i++)
{
int k=getid(wi[i]/p[j]);
g[i]=((g[i]-p[j]*p[j]%mod*(g[k]-sum2[j-1])%mod)%mod+mod)%mod;
h[i]=((h[i]-p[j]*(h[k]-sum[j-1])%mod)%mod+mod)%mod;
}
}
ll ans=s(n,1);
printf("%lld\n",(ans+1)%mod);
return 0;
}