#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int main()
{
  int n;
  cin >> n;
  vector<double> dp(n + 1, -1);
  dp[0] = dp[1] = 0;
  auto dfs = [&](auto f, int now) -> double
  {
    if (dp[now] != -1) return dp[now];
    double sum = 0;
    for (int i = 1; i < now; ++i)
    {
      int nxt = __gcd(i, now);
      sum += f(f, nxt);
    }
    dp[now] = (sum + now) / (now - 1);
    return dp[now];
  };
  printf("%.10f\n", dfs(dfs, n));
}