#include <map>
#include <set>
#include <array>
#include <cmath>
#include <deque>
#include <bitset>
#include <random>
#include <string>
#include <vector>
#include <cassert>
#include <complex>
#include <iomanip>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#include <unordered_set>

using namespace std;

const int MAXN = 1e5 + 100;
int mn[MAXN];
vector<int> dv[MAXN];
vector<int> prdiv[MAXN];

double p[MAXN], q[MAXN], s[MAXN];

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

    cout << fixed << setprecision(20);

    int n;
    cin >> n;
    vector<int> prm;
    for (int i = 2; i <= n; ++i) {
        if (mn[i] == 0) {
            mn[i] = i;
            prm.push_back(i);
            prdiv[i] = {i};
        }
        for (int p : prm) {
            if (p > mn[i] || p * i >= MAXN) break;
            mn[p * i] = p;
            prdiv[p * i] = prdiv[i];
            if (p != mn[i]) {
                prdiv[p * i].push_back(p);
            }
        }
    }

    for (int a = 1; a <= n; ++a) {
        for (int b = a; b <= n; b += a) {
            dv[b].push_back(a);
        }
    }

    int sum = 0;
    for (int i = 1; i <= n; ++i) {
        int inp;
        cin >> inp;
        /// inp = 1;
        p[i] = inp;
        sum += inp;
    }
    for (int i = 1; i <= n; ++i) {
        p[i] /= sum;
        for (int j = i; j <= n; j += i) {
            s[j] += p[i];
        }
    }

    q[1] = 1;
    double ans = -1;
    for (int da1 = 1; da1 <= n; ++da1) {
        q[da1] /= (1 - s[da1]);
        ans += q[da1];
        for (int b1 = 2; b1 * da1 <= n; ++b1) {
            int g = __gcd(da1, b1);
            int d0 = 1;
            int da2 = da1;
            for (int p : prdiv[g]) {
                while (da2 % p == 0) {
                    da2 /= p;
                    d0 *= p;
                }
            }
            for (int d1 : dv[da1 / d0]) {
                int d = d0 * d1;
                q[da1 * b1] += q[da1] * p[d * b1];
            }
        }
    }

    cout << ans << "\n";
    
    return 0;
}