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 MOD = 1e9 + 7;
  const int N = 1e5 + 5;
  int n, a[N], phi[N], cnt[N];
  vector<int> f[N];
  int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    for (int i = 1; i <= N; ++i)
      for (int j = 1; j <= N / i; ++j) f[i * j].push_back(i);
    for (int i = 1; i <= N; ++i) {
      phi[i] = i;
      for (auto u : f[i])
        if (u != i) phi[i] -= phi[u];
    }
    cin >> n;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    long long ans = 0;
    memset(cnt, 0, sizeof(cnt));
    for (int x = 1; x <= n; ++x) {
      vector<int> res;
      for (int i = 1; i <= n / x; ++i) {
        for (auto y : f[a[i * x]]) {
          if (cnt[y] == 0) res.push_back(y);
          cnt[y]++;
        }
      }
      for (auto y : res) {
        ans =
            (ans + ((1LL * phi[x] * phi[y]) % MOD * cnt[y]) % MOD * cnt[y]) % MOD;
        cnt[y] = 0;
      }
    }
    cout << ans;
  }
  