#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 1'000'000'007;
using Mint = ModInt<MO>;


constexpr int MAX = 5010;

int N;
int A[MAX];

int M;
int G[MAX][MAX];
int phi[MAX];

/*
  ([u = v] \sum[w] gcd(A[u], A[w])) - (gcd(A[u], A[v]))
  
  gcd(A[u], A[v]) = \sum[i] [i | A[u]] [i | A[v]] phi(i)
  
  U[u][i] := [i | A[u]]
  V[u][i] := [i | A[v]] phi(i)
  
  V^T D U
  = (\sum[u] V[u][i] deg[u]^-1 U[u][j])
  = (phi[i] \sum[u] [lcm(i, j) | A[u]] deg[u]^-1)
*/
Mint ds[MAX];
Mint prodL[MAX], prodR[MAX];
Mint sums[MAX];
Mint f[MAX][MAX];

int jsLen;
int js[MAX];

int main() {
  for (; ~scanf("%d", &N); ) {
    for (int u = 0; u < N; ++u) {
      scanf("%d", &A[u]);
    }
    sort(A, A + N);
    
    M = A[N - 1];
    for (int i = 1; i <= M; ++i) for (int j = 1; j <= i; ++j) {
      G[i][j] = G[j][i] = (i % j != 0) ? G[i % j][j] : j;
    }
// for(int i=1;i<=M;++i)for(int j=1;j<=M;++j)assert(G[i][j]==__gcd(i,j));
    iota(phi, phi + (M + 1), 0);
    for (int p = 2; p <= M; ++p) if (phi[p] == p) {
      for (int i = p; i <= M; i += p) (phi[i] /= p) *= (p - 1);
    }
// cerr<<"phi = ";pv(phi,phi+M+1);
    
    // remove vertex (N-1)
    fill(ds, ds + N, 0);
    for (int u = 0; u < N; ++u) {
      for (int v = 0; v < N; ++v) {
        ds[u] += G[A[u]][A[v]];
      }
    }
// cerr<<"ds = ";pv(ds,ds+N);
    fill(sums, sums + (M + 1), 0);
    for (int u = 0; u < N - 1; ++u) {
      const Mint invD = ds[u].inv();
      for (int l = 1; l <= M; ++l) if (A[u] % l == 0) {
        sums[l] += invD;
      }
    }
    
    for (int i = 1; i <= M; ++i) for (int j = 1; j <= M; ++j) {
      // f[i][j] = 0;
      f[i][j] = (i == j) ? 1 : 0;
    }
    for (int i = 1; i <= M; ++i) for (int j = 1; j <= M; ++j) {
      const int l = i / G[i][j] * j;
      if (l <= M) {
        // f[i][j] += phi[i] * sums[l];
        f[i][j] -= phi[i] * sums[l];
      }
    }
// for(int i=1;i<=M;++i)pv(f[i]+1,f[i]+M+1);
    
    Mint ans = 1;
    for (int u = 0; u < N - 1; ++u) {
      ans *= ds[u];
    }
    for (int k = M; k >= 1; --k) {
      for (int i = k; i >= 1; --i) if (f[i][k]) {
        // swap(f[k], f[i]);
        for (int j = 1; j <= k; ++j) {
          swap(f[k][j], f[i][j]);
        }
        if (k != i) {
          ans = -ans;
        }
        break;
      }
      ans *= f[k][k];
      if (!ans) {
        break;
      }
      const Mint r = f[k][k].inv();
      jsLen = 0;
      for (int j = k; --j >= 1; ) if (f[k][j]) {
        f[k][j] *= r;
        js[jsLen++] = j;
      }
      for (int i = k; --i >= 1; ) if (f[i][k]) {
        for (int h = 0; h < jsLen; ++h) {
          const int j = js[h];
          f[i][j] -= f[i][k] * f[k][j];
        }
      }
    }
    printf("%u\n", ans.x);
  }
  return 0;
}