#pragma GCC target("avx2") #pragma GCC optimize("Ofast,unroll-loops") #include #include #define rep(i, n) for (int i = 0; i < n; i++) #define per(i, n) for (int i = n - 1; i >= 0; i--) #define ALL(a) a.begin(), a.end() typedef long double ldouble; #undef long #define long long long #define ll long #define vec vector using namespace std; using mint = atcoder::modint; ostream &operator<<(ostream &os, mint a) { return os << a.val(); } template ostream &operator<<(ostream &os, vector &a) { const int n = a.size(); rep(i, n) { os << a[i]; if (i + 1 != n) os << " "; } return os; } template ostream &operator<<(ostream &os, array &a) { rep(i, n) os << a[i] << " \n"[i + 1 == n]; return os; } template istream &operator>>(istream &is, vector &a) { for (T &i : a) is >> i; return is; } template bool chmin(T &x, T y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, T y) { if (x < y) { x = y; return true; } return false; } ldouble harmonic(long n) { if (n <= 1e3) { ldouble ans = 0; for (long i = 1; i <= n; i++) ans += 1.0 / i; return ans; } ldouble ans = log(n) + 0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495; ans += 1.0 / (2 * n); if (n <= 1e8) ans -= 1.0 / (12 * n * n); if (n <= 1e5) ans += 1.0 / (24 * n * n * n); return ans; } void solve() { long n; cin >> n; if (n <= 1e8 + 2024) { ldouble ans = 0; for (long i = 1; i <= n; i++) { for (long j = i; j <= n; j += i) { ans += 1.0 / j; } } cout << ans << endl; return; } const long nn = (int)sqrt(n); ldouble ans = 0; for (long i = 1; i <= nn; i++) { ans += harmonic(n / i) / i; ans += harmonic(i) * (harmonic(n / i) - harmonic(n / (i + 1))); } cout << ans << endl; } int main() { // srand((unsigned)time(NULL)); cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(400); int t = 1; // cin >> t; while (t--) solve(); return 0; }