欧拉函数求和
Description
给出一个数字N，求sigma(phi(i)),1<=i<=N
Input
正整数N。N<=2*10^9
Output
输出答案。
Sample Input
10
Sample Output
32
HINT
直接大力杜教筛
sum_{i=1}^{n}varphi(i) = frac{ntimes(n 1)}{2} - sum_{d=2}^{n}sum_{i=1}^{lfloorfrac{n}{d}rfloor}varphi(i)
代码语言：javascript复制#include<cstdio>
#include<map>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
#define LL long long
using namespace std;
using namespace __gnu_pbds;
const int MAXN=5000030;
int N,limit=5000000,tot=0,vis[MAXN],prime[MAXN];
LL phi[MAXN];
gp_hash_table<int,LL>Aphi;
void GetPhi()
{
vis[1]=1;phi[1]=1;
for(int i=1;i<=limit;i )
{
if(!vis[i]) prime[ tot]=i,phi[i]=i-1;
for(int j=1;j<=tot&&i*prime[j]<=limit;j )
{
vis[i*prime[j]]=1;
if(i%prime[j]==0) {phi[i*prime[j]]=phi[i]*prime[j];break;}
else phi[i*prime[j]]=phi[i]*(prime[j]-1);
}
}
for(int i=1;i<=limit;i ) phi[i] =phi[i-1];
}
LL SolvePhi(LL n)
{
if(n<=limit) return phi[n];
if(Aphi[n]) return Aphi[n];
LL tmp=n*(n 1)/2;
for(int i=2,nxt;i<=n;i=nxt 1)
{
nxt=min(n,n/(n/i));
tmp-=SolvePhi(n/i)*(LL)(nxt-i 1);
}
return Aphi[n]=tmp;
}
int main()
{
GetPhi();
scanf("%lld",&N);
printf("%lld",SolvePhi(N));
return 0;
}
