#include <iostream> // cout, endl, cin
#include <iterator>
#include <string> // string, to_string, stoi
#include <vector> // vector
#include <algorithm> // min, max, swap, sort, reverse, lower_bound, upper_bound
#include <utility> // pair, make_pair
#include <tuple> // tuple, make_tuple
#include <cstdint> // int64_t, int*_t
#include <cstdio> // printf
#include <map> // map
#include <queue> // queue, priority_queue
#include <set> // set
#include <stack> // stack
#include <deque> // deque
#include <unordered_map> // unordered_map
#include <unordered_set> // unordered_set
#include <bitset> // bitset
#include <cctype> // isupper, islower, isdigit, toupper, tolower
#include <iomanip>
#include <climits>
#include <cmath>
#include <functional>
#include <numeric>
#include <regex>
#include <array>
#include <fstream>
#include <sstream>
// #include <atcoder/dsu>

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define repl(i,l,r) for (int i = l; i < (int)(r); i++)
#define all(a) a.begin(),a.end()
#define Pii pair<int,int>
#define Pll pair<long,long>
#define INFi 1000000001
#define INFl 1000000000000000001
using namespace std;

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

template<class T> void printArray(vector<T>&A){
    for(T&a:A){
        cout<<a<<" ";
    }
    cout<<endl;
}
template<class T> void printArrayln(vector<T>&A){
    for(T&a:A){
        cout<<a<<endl;
    }
}


template<class T1,class T2> std::ostream &operator<<(std::ostream &out, const pair<T1,T2> &A){
    cout<<"{"<<A.first<<","<<A.second<<"}";
    return out;
}

template<class T1,class T2> std::ostream &operator<<(std::ostream &out, const map<T1,T2> &M){
    for(const auto&A:M){
        cout<<"{"<<A.first<<","<<A.second<<"}";
    }
    return out;
}

template<class T1> std::ostream &operator<<(std::ostream &out, const set<T1> &M){
    cout<<"{";
    for(const auto&A:M){
        cout<<A<<", ";
    }
    cout<<"}"<<endl;
    return out;
}


template<class T1> std::ostream &operator<<(std::ostream &out, const multiset<T1> &M){
    cout<<"{";
    for(const auto&A:M){
        cout<<A<<", ";
    }
    cout<<"}"<<endl;
    return out;
}

template<class T> std::ostream &operator<<(std::ostream &out, const vector<T> &A){
    for(const T &a:A){
        cout<<a<<" ";
    }
    return out;
}

void print() { cout << endl; }

template <typename Head, typename... Tail>
void print(Head H, Tail... T) {
  cout << H << " ";
  print(T...);
}


template<class T> std::istream &operator>>(std::istream &in,vector<T>&A){
    for(T&a:A){
        std::cin>>a;
    }
    return in;
}


// modint: mod 計算を int を扱うように扱える構造体
template<int MOD> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() { return MOD; }
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};


using mint = Fp<998244353>;

int main(void){
    std::cin.tie(0)->sync_with_stdio(0);
    int N;cin>>N;

    // Nの階乗に、それぞれの素因数がいくつ含まれているか
    vector<int> cnt;
    vector<int> numbers(N+1);
    rep1(i,N)numbers[i]=i;
    for(int i=2;i<=N;i++){
        if(numbers[i]==1)continue;
        cnt.push_back(0);
        for(int j=i;j<=N;j+=i){
            while(numbers[j]%i==0){
                numbers[j]/=i;
                cnt.back()++;
            }
        }
    }

    int prev = -1;
    vector<int> cnt2;
    vector<int> num;
    for(auto&c:cnt){
        if(c==prev){
            cnt2.back()++;
        }else{
            prev = c;
            cnt2.push_back(1);
            num.push_back(c);
        }
    }

    mint sum = 1;
    mint ans = 0;
    for(int i=1000000;i>=1;i--){
        mint tmp = 1;
        rep(j, cnt2.size()){
            if(num[j]/i==0)break;
            tmp *= modpow(mint(num[j]/i+1), cnt2[j]);
        }
        tmp -= sum;
        sum += tmp;
        ans += tmp * mint(i); 
    }
    cout<<ans<<endl;
}