#include<bits/stdc++.h>
using namespace std;
using ll=long long;
constexpr int MOD=998244353;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,l,r) for(int i=(l);i<(int)(r);i++)

int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N;
  cin>>N;
  vector phi(N+1,0.0);
  for(int i=0;i<=N;i++)phi[i]=i;
  for(int i=2;i<=N;i++){
    if(phi[i]!=i)continue;
    for(int j=i;j<=N;j+=i){
      phi[j]=phi[j]/i*(i-1);
    }
  }

  vector dp(N+1,0.0);
  for(int i=1;i<=N;i++){
    if(i>1)dp[i]=(1+dp[i]*i)/(double)(i-1);
    for(int j=2;j*i<=N;j++){
      dp[j*i]+=phi[j]*(dp[i]+1)/((double)j*i);
    }
  }
  cout<<setprecision(10)<<dp[N]<<'\n';
}