mobius_func.cpp

#ifdef DEBUG_IS_VALID
#define DEB 1 
#define _LIBCPP_DEBUG 0
#else
#define DEB 0
#define NDEBUG
#endif

#include "bits/stdc++.h"

#define ALL(g) (g).begin(),(g).end()
#define REP(i, x, n) for(int i = x; i < n; i++)
#define rep(i,n) REP(i,0,n)
#define RREP(i, x, n) for(int i = x; i >= n; i--)
#define rrep(i, n) RREP(i,n,0)
#define pb push_back
#pragma GCC optimize ("-O3")

using namespace std;

#define DUMPOUT cout
#define dump(...) if(DEB) DUMPOUT<<"  "<<#__VA_ARGS__<<" :["<<__LINE__<<":"<<__FUNCTION__<<"]"<<endl<<"    "; if(DEB) dump_func(__VA_ARGS__)
template<typename T1,typename T2>ostream& operator << (ostream& os, pair<T1,T2> p){cout << "(" << p.first << ", " << p.second << ")"; return os;}
template<typename T>ostream& operator << (ostream& os, vector<T>& vec) { os << "{"; for (int i = 0; i<vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : ", "); os << "}"; return os; }
template<typename T>ostream& operator << (ostream& os, set<T>& st){cout << "{"; for(auto itr = st.begin(); itr != st.end(); itr++) cout << *itr << (next(itr)!=st.end() ? ", " : ""); cout << "}"; return os;}
template<typename T1,typename T2>ostream& operator << (ostream& os, map<T1,T2> mp){cout << "{"; for(auto itr = mp.begin(); itr != mp.end(); itr++) cout << "(" << (itr->first) << ", " << (itr->second) << ")" << (next(itr)!=mp.end() ? "," : ""); cout << "}"; return os; }

void dump_func(){DUMPOUT << endl;}
template <class Head, class... Tail>void dump_func(Head&& head, Tail&&... tail){ DUMPOUT << head; if (sizeof...(Tail) == 0) { DUMPOUT << " "; } else { DUMPOUT << ", "; } dump_func(std::move(tail)...);}
template<class T> inline bool chmax(T& a,T const& b){if(a>=b) return false; a=b; return true;}
template<class T> inline bool chmin(T& a,T const& b){if(a<=b) return false; a=b; return true;}
void _main();
int main(){ cin.tie(0); ios::sync_with_stdio(false); _main(); return 0;}

using ll = long long;
using P = pair<int,int>;
using Pl = pair<ll,ll>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;

const int mod=1e9+7,INF=1<<29;
const double EPS=1e-5,PI=3.1415926535897932384626;
const ll lmod = 1e9+7,LINF=1LL<<59; 

struct UnionFindTree{
  vector<int> par,rank,size;
  UnionFindTree(int N){
    par = rank = vector<int>(N,0);
    size = vector<int>(N,1);
    for(int i = 0; i < N; i++) par[i] = i;
  }
  int find(int x){
    if(par[x] == x) return x;
    else return par[x] = find(par[x]);
  }
  void unite(int x,int y){
    x = find(x);
    y = find(y);
    if(x == y)  return ;
    if(rank[x] < rank[y]){
      par[x] = y;
    }else{
      par[y] = x;
      if(rank[x] == rank[y]) ++rank[x];
    }
    size[x] = size[y] = size[x] + size[y];
  }
  bool same(int x,int y){
    return find(x) == find(y);
  }
};

template<int MOD> struct ModInt {
  static const int Mod = MOD; unsigned x; ModInt() : x(0) { }
  ModInt(signed sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
  ModInt(signed long long sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
  int get() const { return (int)x; }
  ModInt &operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; }
  ModInt &operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
  ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; }
  ModInt &operator/=(ModInt that) { return *this *= that.inverse(); }
  ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
  ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
  ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
  ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
  ModInt inverse() const { long long a = x, b = MOD, u = 1, v = 0;
      while (b) { long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); }
      return ModInt(u); }
  bool operator==(ModInt that) const { return x == that.x; }
  bool operator!=(ModInt that) const { return x != that.x; }
  ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; }
};
template<int MOD> ostream& operator<<(ostream& st, const ModInt<MOD> a) { st << a.get(); return st; };
template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) {
  ModInt<MOD> r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r; }
template<typename T, int FAC_MAX> struct Comb { vector<T> fac, ifac;
  Comb(){fac.resize(FAC_MAX,1);ifac.resize(FAC_MAX,1); for(int i = 1; i < FAC_MAX; i++)fac[i]=fac[i-1]*i;
    ifac[FAC_MAX-1]=T(1)/fac[FAC_MAX-1];for(int i = FAC_MAX-2; i >= 1; i--)ifac[i]=ifac[i+1]*T(i+1);}
    T aPb(int a, int b) { if (b < 0 || a < b) return T(0); return fac[a] * ifac[a - b]; }
    T aCb(int a, int b) { if (b < 0 || a < b) return T(0); return fac[a] * ifac[a - b] * ifac[b]; }
    T nHk(int n, int k) { if (n == 0 && k == 0) return T(1); if (n <= 0 || k < 0) return 0;
    return aCb(n + k - 1, k); }}; // nHk = (n+k-1)Ck : n is separator

using mint =  ModInt<int(1e9+7)>;
// using mint = double;
using vm =  vector<mint>;

void _main(){
  ll K; cin >> K ;
  vector<bool> is_prime(K+1,true);
  vi mob(K+1,-1);
  is_prime[0] = is_prime[1] = false;
  mob[0] = mob[1] = 0;
  REP(i,1,K+1){
    if(!is_prime[i]) continue;
    for(int j = 2*i; j <= K; j += i) is_prime[j] = false;
    for(int j = i; j <= K; j += i){
      mob[j] *= -1;
      if(j%(i*i)==0) mob[j] = 0;
    }
  }
  mint ans = 1;
  dump(mob);
  REP(i,2,K+1){
    int num = K/i;
    ans += mint(mob[i])*mint(num)/mint(K-num);
  }
  cout << ans << endl;
}