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;
  const int MAX = 1e5 + 7;
  const int MOD = 1e9 + 7;
  int E[MAX];
  void euler() {
    E[1] = 1;
    for (int i = 2; i < MAX; i++) {
      if (!E[i])
        for (int j = i; j < MAX; j += i) {
          if (!E[j]) E[j] = j;
          E[j] = E[j] / i * (i - 1);
        }
    }
  }
  int n;
  int a[MAX], cnt[MAX];
  vector<int> G[MAX];
  int main() {
    ios::sync_with_stdio(false), cin.tie(NULL);
    euler();
    for (int i = 1; i <= 100000; i++)
      for (int j = 1; j <= sqrt(i); j++)
        if (i % j == 0) {
          G[i].push_back(j);
          if (j * j != i) G[i].push_back(i / j);
        }
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> a[i];
    long long ans = 0;
    for (int i = 1; i <= n; i++) {
      vector<int> v;
      for (int j = i; j <= n; j += i) {
        for (int k : G[a[j]]) {
          if (!cnt[k]) v.push_back(k);
          cnt[k]++;
        }
      }
      for (int j : v) {
        ans += 1ll * E[i] * E[j] % MOD * cnt[j] % MOD * cnt[j] % MOD, ans %= MOD;
        cnt[j] = 0;
      }
    }
    cout << ans << '\n';
    return 0;
  }
  