[欧拉函数] Bzoj P2226 LCMSum

Description

Given n, calculate the sum LCM(1,n) + LCM(2,n) + .. + LCM(n,n), where LCM(i,n) denotes the Least Common Multiple of the integers i and n.

题解

代码

#include <cstdio>
#include <iostream>
#define N 1000010
#define ll long long
using namespace std;
ll T,bz[N],phi[N],q[N],ans[N];
int main()
{
    scanf("%lld",&T),phi[1]=1;
    for (ll i=2;i<=N;i++)
    {
        if (!bz[i]) q[++q[0]]=i,phi[i]=i-1;
        for (ll j=1;j<=q[0]&&i*q[j]<=N;j++)
            if (i*q[j]<N)
            {
                bz[i*q[j]]=1;
                if (i%q[j]==0) { phi[i*q[j]]=phi[i]*q[j]; break; }
                phi[i*q[j]]=phi[i]*(q[j]-1);
            }
    }
    for (int i=1;i<=N;i++) for (int j=1;i*j<=N;j++) ans[i*j]+=j*phi[j]/2;
    for (ll i=1;i<=N;i++) ans[i]=i*ans[i]+i;
    for (ll i=1,x;i<=T;i++) scanf("%lld",&x),printf("%lld
",ans[x]);
}