// Original C++ solution (slower):
#pragma GCC optimize("Ofast")

#include<bits/stdc++.h>

// #include<ext/pb_ds/assoc_container.hpp>

// #include<ext/pb_ds/tree_policy.hpp>

// #include<ext/pb_ds/tag_and_trait.hpp>

// using namespace __gnu_pbds;

// #include<boost/multiprecision/cpp_int.hpp>

// namespace multiprecisioninteger = boost::multiprecision;

// using cint=multiprecisioninteger::cpp_int;

using namespace std;

using ll=long long;

#define double long double

using datas=pair<ll,ll>;

using ddatas=pair<double,double>;

using tdata=pair<ll,datas>;

using vec=vector<ll>;

using mat=vector<vec>;

using pvec=vector<datas>;

using pmat=vector<pvec>;

// using llset=tree<ll,null_type,less<ll>,rb_tree_tag,tree_order_statistics_node_update>;

#define For(i,a,b) for(i=a;i<(ll)b;i++)

#define bFor(i,b,a) for(i=b-1;i>=(ll)a;i--)

#define rep(i,N) For(i,0,N)

#define rep1(i,N) For(i,1,N)

#define brep(i,N) bFor(i,N,0)

#define all(v) (v).begin(),(v).end()

#define allr(v) (v).rbegin(),(v).rend()

#define vsort(v) sort(all(v))

#define vrsort(v) sort(allr(v))

#define endl "\n"

#define pb push_back

#define eb emplace_back

#define print(v) cout<<v<<endl

#define printyes cout<<"Yes"<<endl

#define printno cout<<"No"<<endl

#define printYES cout<<"YES"<<endl

#define printNO cout<<"NO"<<endl

#define output(v) do{bool f=0;for(auto outi:v){cout<<(f?" ":"")<<outi;f=1;}cout<<endl;}while(0)

const ll mod=1000000007;

// const ll mod=998244353;

const ll inf=1LL<<60;

const double PI = acos(-1);

const double eps = 1e-9;

template<class T> inline bool chmax(T& a,T b){bool x=a<b;if(x)a=b;return x;} 

template<class T> inline bool chmin(T& a,T b){bool x=a>b;if(x)a=b;return x;} 



void startupcpp(){

  cin.tie(0);

  ios::sync_with_stdio(false);

  cout<<fixed<<setprecision(15);

}



double distance(ddatas x,ddatas y){

  double a=x.first-y.first,b=x.second-y.second;

  return sqrt(a*a+b*b);

}



ll modinv(ll a) {

  ll b=mod,u=1,v=0,t;

  while(b){

    t=a/b;

    a-=t*b; swap(a,b);

    u-=t*v; swap(u,v);

  }

  return (u+mod)%mod;

}



ll moddevide(ll a,ll b){return (a*modinv(b))%mod;}



vec modncrlistp,modncrlistm;



ll modncr(ll n,ll r){

  if(n<r)return 0;

  ll i,size=modncrlistp.size();

  if(size<=n){

    modncrlistp.resize(n+1);

    modncrlistm.resize(n+1);

    if(!size){

      modncrlistp[0]=modncrlistm[0]=1;

      size++;

    }

    For(i,size,n+1){

      modncrlistp[i]=modncrlistp[i-1]*i%mod;

      modncrlistm[i]=modinv(modncrlistp[i]);

    }

  }

  return modncrlistp[n]*modncrlistm[r]%mod*modncrlistm[n-r]%mod;

}



ll modpow(ll a,ll n){

  ll res=1;

  while(n>0){

    if(n&1)res=res*a%mod;

    a=a*a%mod;

    n>>=1;

  }

  return res;

}



ll gcd(ll a,ll b){if(!b)return a;return (a%b==0)?b:gcd(b,a%b);}

ll lcm(ll a,ll b){return a/gcd(a,b)*b;}



ll countdigits(ll n){

  ll ans=0;

  while(n){n/=10;ans++;}

  return ans;

}



ll sumdigits(ll n){

  ll ans=0;

  while(n){ans+=n%10;n/=10;}

  return ans;

}



int main(){

  // startupcpp();

  // int codeforces;cin>>codeforces;while(codeforces--){

  ll i,j,k,N,H,W,ans=0;

  string s;

  cin>>N;++N;

  rep1(i,N)rep1(j,N)rep1(k,N){

    ans+=gcd(gcd(i,j),k);

  }

  print(ans);

  return 0;

}

// Optimized solution to the same problem (faster):
#pragma GCC optimize("Ofast")

#include<bits/stdc++.h>

// #include<ext/pb_ds/assoc_container.hpp>

// #include<ext/pb_ds/tree_policy.hpp>

// #include<ext/pb_ds/tag_and_trait.hpp>

// using namespace __gnu_pbds;

// #include<boost/multiprecision/cpp_int.hpp>

// namespace multiprecisioninteger = boost::multiprecision;

// using cint=multiprecisioninteger::cpp_int;

using namespace std;

using ll=long long;

#define double long double

using datas=pair<ll,ll>;

using ddatas=pair<double,double>;

using tdata=pair<ll,datas>;

using vec=vector<ll>;

using mat=vector<vec>;

using pvec=vector<datas>;

using pmat=vector<pvec>;

// using llset=tree<ll,null_type,less<ll>,rb_tree_tag,tree_order_statistics_node_update>;

#define For(i,a,b) for(i=a;i<(ll)b;i++)

#define bFor(i,b,a) for(i=b-1;i>=(ll)a;i--)

#define rep(i,N) For(i,0,N)

#define rep1(i,N) For(i,1,N)

#define brep(i,N) bFor(i,N,0)

#define all(v) (v).begin(),(v).end()

#define allr(v) (v).rbegin(),(v).rend()

#define vsort(v) sort(all(v))

#define vrsort(v) sort(allr(v))

#define endl "\n"

#define pb push_back

#define eb emplace_back

#define print(v) cout<<v<<endl

#define printyes cout<<"Yes"<<endl

#define printno cout<<"No"<<endl

#define printYES cout<<"YES"<<endl

#define printNO cout<<"NO"<<endl

#define output(v) do{bool f=0;for(auto outi:v){cout<<(f?" ":"")<<outi;f=1;}cout<<endl;}while(0)

const ll mod=1000000007;

// const ll mod=998244353;

const ll inf=1LL<<60;

const double PI = acos(-1);

const double eps = 1e-9;

template<class T> inline bool chmax(T& a,T b){bool x=a<b;if(x)a=b;return x;} 

template<class T> inline bool chmin(T& a,T b){bool x=a>b;if(x)a=b;return x;} 



void startupcpp(){

  cin.tie(0);

  ios::sync_with_stdio(false);

  cout<<fixed<<setprecision(15);

}



double distance(ddatas x,ddatas y){

  double a=x.first-y.first,b=x.second-y.second;

  return sqrt(a*a+b*b);

}



ll modinv(ll a) {

  ll b=mod,u=1,v=0,t;

  while(b){

    t=a/b;

    a-=t*b; swap(a,b);

    u-=t*v; swap(u,v);

  }

  return (u+mod)%mod;

}



ll moddevide(ll a,ll b){return (a*modinv(b))%mod;}



vec modncrlistp,modncrlistm;



ll modncr(ll n,ll r){

  if(n<r)return 0;

  ll i,size=modncrlistp.size();

  if(size<=n){

    modncrlistp.resize(n+1);

    modncrlistm.resize(n+1);

    if(!size){

      modncrlistp[0]=modncrlistm[0]=1;

      size++;

    }

    For(i,size,n+1){

      modncrlistp[i]=modncrlistp[i-1]*i%mod;

      modncrlistm[i]=modinv(modncrlistp[i]);

    }

  }

  return modncrlistp[n]*modncrlistm[r]%mod*modncrlistm[n-r]%mod;

}



ll modpow(ll a,ll n){

  ll res=1;

  while(n>0){

    if(n&1)res=res*a%mod;

    a=a*a%mod;

    n>>=1;

  }

  return res;

}



ll gcd(ll a,ll b){if(!b)return a;return (a%b==0)?b:gcd(b,a%b);}

ll lcm(ll a,ll b){return a/gcd(a,b)*b;}



ll countdigits(ll n){

  ll ans=0;

  while(n){n/=10;ans++;}

  return ans;

}



ll sumdigits(ll n){

  ll ans=0;

  while(n){ans+=n%10;n/=10;}

  return ans;

}



int main(){

  // startupcpp();

  // int codeforces;cin>>codeforces;while(codeforces--){

  ll i,j,N=3,K,ans=0;

  cin>>K;++K;

  mat g(K);

  vec v(K,0);

  rep1(i,K)for(j=i;j<K;j+=i){

    g[i].eb(j);

  }

  for(i=K-1;i>0;i--){

    v[i]=modpow(g[i].size(),N);

    rep1(j,g[i].size())v[i]-=v[g[i][j]];

    v[i]=(mod+v[i]%mod)%mod;

  }

  rep(i,K){

    (ans+=v[i]*i%mod)%=mod;

  }

  // output(v);

  print(ans);

}


// Fastest known solution for this problem: