#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); }
istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } 

typedef long long ll;
typedef vector<vector<int>> Graph;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define FOR(i,l,r) for (int i = l;i < (int)(r); i++)
#define rep(i,n) for (int i = 0;i < (int)(n); i++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define my_sort(x) sort(x.begin(), x.end())
#define my_max(x) *max_element(all(x))
#define my_min(x) *min_element(all(x))
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const int INF = (1<<30) - 1;
const ll LINF = (1LL<<62) - 1;
const int MOD = 998244353;
const int MOD2 = 1e9+7;
const double PI = acos(-1);
vector<int> di = {1,0,-1,0};
vector<int> dj = {0,1,0,-1};

#ifdef LOCAL
#  include <debug_print.hpp>
#  define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define debug(...) (static_cast<void>(0))
#endif

vector<int> make_divisors(int n){
    vector<int> divisors;
    int i = 1;
    while (i * i <= n){
        if (n % i == 0){
            divisors.push_back(i);
            if (i != (n/i)) divisors.push_back(n/i);
        }
        i++;
    }
    sort(all(divisors));
    return divisors;
}

int main(){
    cin.tie(0);
    ios_base::sync_with_stdio(false);

    int N; cin >> N;
    vector<double> memo(N + 1, -1);
    vector<int> cnt(N + 1, 0);

    memo[1] = 0;
    function<double(int)> dp = [&](int x){
        if(memo[x] >= 0.0) return memo[x];

        vector<int> divs = make_divisors(x);
        divs.pop_back();
        reverse(all(divs));

        double acc = 0.0;
        for(auto &p : divs){
            cnt[p] = (x - 1) / p;
            for(auto &q : divs){
                if(q > p && q % p == 0) cnt[p] -= cnt[q];
            }

            acc += cnt[p] * dp(p);
        }
        memo[x] = (acc / (double)x + 1) * (double)x / (double)(x - 1);
        return memo[x];
    };

    cout << fixed << setprecision(15) << dp(N) << endl;
}