/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author zjsdut
 */

#ifndef ALGO_UTILS
#define ALGO_UTILS
#include <algorithm>
#include <iomanip>
#include <iostream>
#include <vector>
struct fast_ios {
  fast_ios() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(10);
  };
} fast_ios_;

template <typename A, typename B> bool chkmin(A &a, const B &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

template <typename A, typename B> bool chkmax(A &a, const B &b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}

template <typename T>
std::istream &operator>>(std::istream &stream, std::vector<T> &vec) {
  for (auto &x : vec)
    stream >> x;
  return stream;
}

void scan() {}

template <class T, class... Args> void scan(T &a, Args &... rest) {
  std::cin >> a;
  scan(rest...);
}

using ll = long long;
using vl = std::vector<ll>;
using vb = std::vector<bool>;
using vi = std::vector<int>;
using pii = std::pair<int, int>;
using pli = std::pair<ll, int>;
template <typename T> using vv = std::vector<std::vector<T>>;
#define rng(i, a, b) for (int i = (int)(a); i < (int)(b); ++i)
#define up(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define down(i, b, a) for (int i = int(b); i >= int(a); i--)
#define TOKENPASTE(x, y) x##y
#define TOKENPASTE2(x, y) TOKENPASTE(x, y)
#define rep(n)                                                                 \
  for (int TOKENPASTE2(_iter_, __LINE__) = 0,                                  \
                               TOKENPASTE2(_num_, __LINE__) = (int)(n);        \
       TOKENPASTE2(_iter_, __LINE__) < TOKENPASTE2(_num_, __LINE__);           \
       ++TOKENPASTE2(_iter_, __LINE__))
#define FOR(x, cont) for (const auto &x : cont)
#define For(x, cont) for (auto &x : cont)
#define all(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ep emplace
#define SZ(x) (int)(x).size()
#define UNIQ(vec) (vec).erase(std::unique(all(vec)), std::end(vec))
#define LB(cont, x) int(std::lower_bound(all(cont), x) - std::begin(cont))
#define UB(cont, x) int(std::upper_bound(all(cont), x) - std::begin(cont))

template <typename T>
std::ostream &operator<<(std::ostream &stream, const std::vector<T> &vec) {
  if (!vec.empty()) {
    stream << vec[0];
    for (size_t i = 1; i != vec.size(); ++i)
      stream << ' ' << vec[i];
  }
  return stream;
}

template <typename T> void print(const std::vector<T> &t) {
  std::cout << t << '\n';
}

template <typename T> void print(const std::vector<std::vector<T>> &t) {
  for (const auto &row : t) {
    print(row);
  }
}

template <typename T> void print(const T &t) { std::cout << t << ' '; }

template <typename T, typename... Args>
void print(const T &t, const Args &... rest) {
  print(t);
  print(rest...);
}

template <typename T> void println(const T &t) { std::cout << t << '\n'; }

template <typename T, typename... Args>
void println(const T &t, const Args &... rest) {
  print(t);
  println(rest...);
}
#endif

using std::to_string;
std::string to_string(const std::string &s) { return '"' + s + '"'; }

std::string to_string(const char *s) { return to_string((std::string)s); }

std::string to_string(bool b) { return (b ? "true" : "false"); }

template <typename A, typename B> std::string to_string(const std::pair<A, B>& p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A> std::string to_string(const A& v) {
  bool first = true;
  std::string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

void debug_out() { std::cerr << std::endl; }

template <typename Head, typename... Tail> void debug_out(const Head& H, const Tail&... T) {
  std::cerr << " " << to_string(H);
  debug_out(T...);
}

#if defined LOCAL
#define debug(...) std::cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

#ifndef ALGO_MODULAR
#define ALGO_MODULAR

#include <cassert>
using std::swap;
// tourist's modular-arithmetic class
template <typename T> T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T> class Modular {
public:
  using Type = typename std::decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}

  template <typename U> Modular(const U &x) { value = normalize(x); }

  template <typename U> static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0)
      v += mod();
    return v;
  }

  const Type &operator()() const { return value; }

  template <typename U> explicit operator U() const {
    return static_cast<U>(value);
  }

  constexpr static Type mod() { return T::value; }

  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod())
      value -= mod();
    return *this;
  }

  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0)
      value += mod();
    return *this;
  }

  template <typename U> Modular &operator+=(const U &other) {
    return *this += Modular(other);
  }

  template <typename U> Modular &operator-=(const U &other) {
    return *this -= Modular(other);
  }

  Modular &operator++() { return *this += 1; }

  Modular &operator--() { return *this -= 1; }

  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }

  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }

  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  std::enable_if_t<std::is_same<typename Modular<U>::Type, int>::value, Modular> &
  operator*=(const Modular &rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x),
        d, m;
    asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod()));
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }

  template <typename U = T>
  std::enable_if_t<std::is_same<typename Modular<U>::Type, int64_t>::value, Modular> &
  operator*=(const Modular &rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
        rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }

  template <typename U = T>
  std::enable_if_t<!std::is_integral<typename Modular<U>::Type>::value, Modular> &
  operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular &operator/=(const Modular &other) {
    return *this *= Modular(inverse(other.value, mod()));
  }

  template <typename U> friend const Modular<U> &abs(const Modular<U> &v) {
    return v;
  }

  template <typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

  template <typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

  template <typename U>
  friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

private:
  Type value;
};

template <typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value == rhs.value;
}

template <typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}

template <typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) == rhs;
}

template <typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template <typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) {
  return !(lhs == rhs);
}

template <typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template <typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value < rhs.value;
}

template <typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template <typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}

template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template <typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template <typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}

template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template <typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template <typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}

template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template <typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template <typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}

template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template <typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1)
      res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template <typename T> bool IsZero(const Modular<T> &number) {
  return number() == 0;
}

template <typename T> std::string to_string(const Modular<T> &number) {
  return to_string(number());
}

template <typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
  return stream << number();
}

template <typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
  typename std::common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

template <int md>
using Mint = Modular<std::integral_constant<std::decay<decltype(md)>::type, md>>;
constexpr int M7 = 1000000007;
constexpr int M3 = 998244353;
using ModType = int;
struct VarMod {
  static ModType value;
};
ModType VarMod::value;
ModType &md = VarMod::value;
using vmint = Modular<VarMod>;
#endif
using namespace std;

class ESumOfGcdOfTuplesHard {
  static void SOLVE() {
    int n = 3, k;
    scan(k);
    using mint = Mint<M7>;
    // dp[i]: n个不超过i的数gcd==1的方案数
    vector<mint> dp(k+1);
    dp[1] = 1;
    up (i, 2, k) {
      dp[i] = power(mint(i), n);
      for (int j = 2; j <= i; ) {
        // max x s.t. i / x == i / j
        int r = i / (i / j);
        assert(r >= j);
        dp[i]-= (r - j + 1) * dp[i / j];
        j = r + 1;
      }
    }
    mint ans = dp[k];
    up (i, 2, k) {
      ans += dp[k / i] * i;
    }
    println(ans);
  }

public:
  static void solve(std::istream &in, std::ostream &out) {
    auto cin_buff = std::cin.rdbuf(in.rdbuf());
    auto cerr_buff = std::cerr.rdbuf(std::cout.rdbuf(out.rdbuf()));
    SOLVE();
    std::cout.rdbuf(std::cerr.rdbuf(cerr_buff));
    std::cin.rdbuf(cin_buff);
  }
};


int main() {
  ESumOfGcdOfTuplesHard solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  solver.solve(in, out);
  return 0;
}


Measured memory_bytes: 3620