description: Mr. Chanek has an array a of n integers. The prettiness value of a is denoted as:
  
  $$$∑_{i=1}^{n} {∑_{j=1}^{n} {\gcd(a_i, a_j) ⋅ \gcd(i, j)}}$$$
  
  where \gcd(x, y) denotes the greatest common divisor (GCD) of integers x and y.
  
  In other words, the prettiness value of an array a is the total sum of \gcd(a_i, a_j) ⋅ \gcd(i, j) for all pairs (i, j).
  
  Help Mr. Chanek find the prettiness value of a, and output the result modulo 10^9 + 7!
  
  Input
  
  The first line contains an integer n (2 ≤ n ≤ 10^5).
  
  The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^5).
  
  Output
  
  Output an integer denoting the prettiness value of a modulo 10^9 + 7.
  
  Example
  
  Input
  
  
  5
  3 6 2 1 4
  
  
  Output
  
  
  77
solution: #include <bits/stdc++.h>
  using namespace std;
  void abc() { cout << endl; }
  template <typename T, typename... U>
  void abc(T a, U... b) {
    cout << a << ' ', abc(b...);
  }
  template <typename T>
  void printv(T l, T r) {
    while (l != r) cout << *l << " \n"[++l == r];
  }
  template <typename A, typename B>
  istream& operator>>(istream& o, pair<A, B>& a) {
    return o >> a.first >> a.second;
  }
  template <typename A, typename B>
  ostream& operator<<(ostream& o, pair<A, B> a) {
    return o << '(' << a.first << ", " << a.second << ')';
  }
  template <typename T>
  ostream& operator<<(ostream& o, vector<T> a) {
    bool is = false;
    for (T i : a) {
      o << (is ? ' ' : '{'), is = true, o << i;
    }
    return o << '}';
  }
  template <typename T>
  struct vv : vector<vector<T>> {
    vv(int n, int m, T v) : vector<vector<T>>(n, vector<T>(m, v)) {}
    vv() {}
  };
  template <typename T>
  struct vvv : vector<vv<T>> {
    vvv(int n, int m, int k, T v) : vector<vv<T>>(n, vv<T>(m, k, v)) {}
    vvv() {}
  };
  const int mod = 1e9 + 7, N = 100087, logN = 20, K = 111;
  vector<int> f[N];
  int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    for (int i = 1; i < N; ++i)
      for (int j = i; j < N; j += i) {
        f[j].push_back(i);
      }
    int n;
    cin >> n;
    vector<int> a(n + 1), phi(N);
    for (int i = 1; i <= n; ++i) {
      cin >> a[i];
    }
    for (int i = 1; i < N; ++i) {
      int x = i;
      phi[i] = i;
      for (int j = 2; j * j <= x; ++j)
        if (x % j == 0) {
          phi[i] -= phi[i] / j;
          while (x % j == 0) x /= j;
        }
      if (x > 1) phi[i] -= phi[i] / x;
    }
    vector<long long int> cnt(N, 0), ans(n + 1, 0);
    for (int d = 1; d <= n; ++d) {
      for (int i = d; i <= n; i += d) {
        for (int j : f[a[i]]) {
          ans[d] += (cnt[j] * 2 + 1) * phi[j] % mod;
          cnt[j]++;
          if (ans[d] >= mod) ans[d] -= mod;
        }
      }
      for (int i = d; i <= n; i += d) {
        for (int j : f[a[i]]) {
          cnt[j]--;
        }
      }
    }
    long long int tans = 0;
    for (int i = n; i > 0; --i) {
      for (int j = i + i; j <= n; j += i) {
        ans[i] -= ans[j];
        if (ans[i] < 0) ans[i] += mod;
      }
      (tans += ans[i] * i) %= mod;
    }
    cout << tans << endl;
  }
  