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 per() { cerr << endl; }
  template <typename Head, typename... Tail>
  void per(Head H, Tail... T) {
    cerr << H << ' ';
    per(T...);
  }
  template <class T>
  bool uin(T& a, T b) {
    return a > b ? (a = b, true) : false;
  }
  template <class T>
  bool uax(T& a, T b) {
    return a < b ? (a = b, true) : false;
  }
  template <class U, class V>
  ostream& operator<<(ostream& out, const pair<U, V>& a) {
    return out << "(" << a.first << ", " << a.second << ")";
  }
  template <class U, class V>
  istream& operator>>(istream& in, pair<U, V>& a) {
    return in >> a.first >> a.second;
  }
  template <typename W,
            typename T = typename enable_if<!is_same<W, string>::value,
                                            typename W::value_type>::type>
  ostream& operator<<(ostream& out, const W& v) {
    out << "{ ";
    for (const auto& first : v) out << first << ", ";
    return out << '}';
  }
  template <class T>
  void readArr(T from, T to) {
    for (auto i = from; i != to; ++i) cin >> *i;
  }
  mt19937 mrand(1337);
  unsigned int myRand32() { return mrand() & (unsigned int)(-1); }
  unsigned long long myRand64() {
    return ((unsigned long long)myRand32() << 32) ^ myRand32();
  }
  const int mod = 1000000007;
  void add(int& a, int b) {
    a += b;
    if (a >= mod) a -= mod;
  }
  void dec(int& a, int b) {
    a -= b;
    if (a < 0) a += mod;
  }
  int mult(int a, int b) { return a * (long long)b % mod; }
  int bp(int a, int b) {
    int res = 1;
    while (b > 0) {
      if (b & 1) res = mult(res, a);
      a = mult(a, a);
      b >>= 1;
    }
    return res;
  }
  const int N = 1e5 + 7;
  vector<int> divs[N];
  int phi[N];
  int calc_phi(int n) {
    int result = n;
    for (int i = 2; i * i <= n; ++i)
      if (n % i == 0) {
        while (n % i == 0) n /= i;
        result -= result / i;
      }
    if (n > 1) result -= result / n;
    return result;
  }
  void init() {
    for (int i = 1; i < N; ++i) {
      for (int j = 1; j * j <= i; ++j) {
        if (i % j == 0) {
          divs[i].push_back(j);
          if (j * j != i) divs[i].push_back(i / j);
        }
      }
      phi[i] = calc_phi(i);
    }
  }
  int cnt[N];
  bool used[N];
  int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    init();
    int n;
    cin >> n;
    vector<int> a(n);
    for (int i = 0; i < n; ++i) {
      cin >> a[i];
    }
    int res = 0;
    for (int first = 1; first <= n; ++first) {
      for (int pos = first; pos <= n; pos += first) {
        for (int d : divs[a[pos - 1]]) {
          ++cnt[d];
        }
      }
      for (int pos = first; pos <= n; pos += first) {
        for (int d : divs[a[pos - 1]]) {
          if (used[d]) continue;
          used[d] = true;
          int tet = cnt[d];
          int now = mult(phi[first], mult(phi[d], tet * (long long)tet % mod));
          add(res, now);
        }
      }
      for (int pos = first; pos <= n; pos += first) {
        for (int d : divs[a[pos - 1]]) {
          --cnt[d];
          used[d] = false;
        }
      }
    }
    cout << res << "\n";
  }
  