题目链接

https://lydsy.com/JudgeOnline/problem.php?id=4805

题解

直接杜教筛筛φ\varphi函数即可。

代码

#include <map>
#include <cstdio>
#include <algorithm>

int read()
{
  int x=0,f=1;
  char ch=getchar();
  while((ch<'0')||(ch>'9'))
    {
      if(ch=='-')
        {
          f=-f;
        }
      ch=getchar();
    }
  while((ch>='0')&&(ch<='9'))
    {
      x=x*10+ch-'0';
      ch=getchar();
    }
  return x*f;
}

const int maxn=1587401;

int p[maxn+10],prime[maxn+10],cnt;
long long phi[maxn+10];

int getprime()
{
  p[1]=phi[1]=1;
  for(int i=2; i<=maxn; ++i)
    {
      if(!p[i])
        {
          prime[++cnt]=i;
          phi[i]=i-1;
        }
      for(int j=1; (j<=cnt)&&(i*prime[j]<=maxn); ++j)
        {
          int x=i*prime[j];
          p[x]=1;
          if(i%prime[j]==0)
            {
              phi[x]=phi[i]*prime[j];
              break;
            }
          phi[x]=phi[i]*(prime[j]-1);
        }
    }
  for(int i=1; i<=maxn; ++i)
    {
      phi[i]+=phi[i-1];
    }
  return 0;
}

std::map<int,long long> mp;

long long getsum(int n)
{
  if(n<=maxn)
    {
      return phi[n];
    }
  if(mp.count(n))
    {
      return mp[n];
    }
  long long ans=1ll*n*(n+1)/2;
  for(int l=2,r; l<=n; l=r+1)
    {
      r=n/(n/l);
      ans-=(r-l+1)*getsum(n/l);
    }
  return mp[n]=ans;
}

int n;

int main()
{
  getprime();
  n=read();
  printf("%lld\n",getsum(n));
  return 0;
}