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
1 #include <cstdio>
2 #include <iostream>
3 #define N 1000010
4 #define ll long long
5 using namespace std;
6 ll T,bz[N],phi[N],q[N],ans[N];
7 int main()
8 {
9 scanf("%lld",&T),phi[1]=1;
10 for (ll i=2;i<=N;i++)
11 {
12 if (!bz[i]) q[++q[0]]=i,phi[i]=i-1;
13 for (ll j=1;j<=q[0]&&i*q[j]<=N;j++)
14 if (i*q[j]<N)
15 {
16 bz[i*q[j]]=1;
17 if (i%q[j]==0) { phi[i*q[j]]=phi[i]*q[j]; break; }
18 phi[i*q[j]]=phi[i]*(q[j]-1);
19 }
20 }
21 for (int i=1;i<=N;i++) for (int j=1;i*j<=N;j++) ans[i*j]+=j*phi[j]/2;
22 for (ll i=1;i<=N;i++) ans[i]=i*ans[i]+i;
23 for (ll i=1,x;i<=T;i++) scanf("%lld",&x),printf("%lld\n",ans[x]);
24 }