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 MAXN = 1e5 + 5;
  const int MOD = 1e9 + 7;
  vector<int> f[MAXN];
  int phi[MAXN];
  int a[MAXN];
  int cnt[MAXN];
  long long calc(vector<int> a) {
    long long sm = 0;
    for (auto x : a) {
      for (auto y : f[x]) {
        int h = (2 * cnt[y] + 1);
        sm = (sm + 1ll * phi[y] * h) % MOD;
        cnt[y] += 1;
      }
    }
    for (auto x : a) {
      for (auto y : f[x]) {
        cnt[y] = 0;
      }
    }
    return sm;
  }
  int main() {
    for (int i = 1; i < MAXN; i++) {
      for (int j = 1; j * i < MAXN; j++) {
        f[i * j].push_back(i);
      }
    }
    phi[1] = 1;
    for (int i = 2; i < MAXN; i++) {
      phi[i] = i;
      for (auto x : f[i]) {
        if (x == i) {
          continue;
        }
        phi[i] -= phi[x];
      }
    }
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
    }
    long long ans = 0;
    for (int j = 1; j <= n; j++) {
      vector<int> cur;
      for (int k = j; k <= n; k += j) {
        cur.push_back(a[k]);
      }
      ans += 1ll * calc(cur) * phi[j] % MOD;
      ans %= MOD;
    }
    cout << ans << "\n";
    return 0;
  }
  