#include <iostream>
#include <string>
#include <stdio.h>
#include <algorithm>
#include <vector>
#include <tuple>
#include <map>
#include<set>
#include<queue>
#include<stack>
#include <unordered_set>
#include<thread>
#include<bits/stdc++.h>

#include <atcoder/all>
#include <cstdio>

// #pragma GCC target("avx")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")

//if(a < 0 || h <= a || b < 0 || w <= b)return;


using namespace std;
using namespace atcoder;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using mint = modint998244353;
using min1 = modint1000000007;
using VL = vector<ll>;
template<typename T> using pq = priority_queue<T>;//降順?(最大取り出し)
template<typename T> using pqg = priority_queue<T, vector<T>, greater<T>>;//昇順?(最小取り出し)
template<typename T> using vector2 = vector<vector<T>>;
template<typename T> using vector3 = vector<vector<vector<T>>>;
template<typename T> using vector4 = vector<vector<vector<vector<T>>>>;
template<typename T> using vector5 = vector<vector<vector<vector<vector<T>>>>>;
template<typename T> using vector6 = vector<vector<vector<vector<vector<vector<T>>>>>>;
template<typename T> using pairs = pair<T,T>;
#define rep(i, n) for (ll i = 0; i < ll(n); i++)
#define rep1(i,n) for(int i = 1;i <= int(n);i++)
#define repm(i, m, n) for (int i = (m); (i) < int(n);(i)++)
#define repmr(i, m, n) for (int i = (m) - 1; (i) >= int(n);(i)--)
#define rep0(i,n) for(int i = n - 1;i >= 0;i--)
#define rep01(i,n) for(int i = n;i >= 1;i--)



// NのK乗根N < 2^64, K <= 64
uint64_t kth_root(uint64_t N, uint64_t K) {
    assert(K >= 1);
    if (N <= 1 || K == 1) return N;
    if (K >= 64) return 1;
    if (N == uint64_t(-1)) --N;
    
    auto mul = [&](uint64_t x, uint64_t y) -> uint64_t {
        if (x < UINT_MAX && y < UINT_MAX) return x * y;
        if (x == uint64_t(-1) || y == uint64_t(-1)) return uint64_t(-1);
        return (x <= uint64_t(-1) / y ? x * y : uint64_t(-1));
    };
    auto power = [&](uint64_t x, uint64_t k) -> uint64_t {
        if (k == 0) return 1ULL;
        uint64_t res = 1ULL;
        while (k) {
            if (k & 1) res = mul(res, x);
            x = mul(x, x);
            k >>= 1;
        }
        return res;
    };
    
    uint64_t res;
    if (K == 2) res = sqrtl(N) - 1;
    else if (K == 3) res = cbrt(N) - 1;
    else res = pow(N, nextafter(1 / double(K), 0));
    while (power(res + 1, K) <= N) ++res;
    return res;
}
// ユークリッドの互除法による最大公約数算出
ll GCD(ll a,ll b){
    if(b == 0)return a;
    return GCD(b, a % b);
}
//拡張ユークリッドの互除法による(ax + by = GCD(a,b))を満たすx,yの算出
pair<long long, long long> extgcd(long long a, long long b) {
  if (b == 0) return make_pair(1, 0);
  long long x, y;
  tie(y, x) = extgcd(b, a % b);
  y -= a / b * x;
  return make_pair(x, y);
}
struct UnionFind {
    vector<int> par; // par[i]:iの親の番号　(例) par[3] = 2 : 3の親が2
    
    UnionFind(int N) : par(N) { //最初は全てが根であるとして初期化
        for(int i = 0; i < N; i++) par[i] = i;
    }
    
    int root(int x) { // データxが属する木の根を再帰で得る：root(x) = {xの木の根}
        if (par[x] == x) return x;
        return par[x] = root(par[x]);
    }
    
    void unite(int x, int y) { // xとyの木を併合
        int rx = root(x); //xの根をrx
        int ry = root(y); //yの根をry
        if (rx == ry) return; //xとyの根が同じ(=同じ木にある)時はそのまま
        par[rx] = ry; //xとyの根が同じでない(=同じ木にない)時：xの根rxをyの根ryにつける
    }
    
    bool same(int x, int y) { // 2つのデータx, yが属する木が同じならtrueを返す
        int rx = root(x);
        int ry = root(y);
        return rx == ry;
    }
};
ll n;

struct UnionFind2 {
    vector2<int> par; // par[i]:iの親の番号　(例) par[3] = 2 : 3の親が2
    
    UnionFind2(int N) : par(N,vector<int>(N)) { //最初は全てが根であるとして初期化
        for(int i = 0; i < N; i++)for(int j = 0;j < N;j++) par[i][j] = i * N + j;
    }
    
    int root(int y,int x) { // データxが属する木の根を再帰で得る：root(x) = {xの木の根}
        if (par[y][x] == y * n + x) return y * n +x;
        return par[y][x] = root(par[y][x] / n,par[y][x] % n);
    }
    
    void unite(int y0, int x0,int y1,int x1) { // xとyの木を併合
        int rx = root(y0,x0); //xの根をrx
        int ry = root(y1,x1); //yの根をry
        if (rx == ry) return; //xとyの根が同じ(=同じ木にある)時はそのまま
        par[rx / n][rx % n] = ry; //xとyの根が同じでない(=同じ木にない)時：xの根rxをyの根ryにつける
    }
    
    bool same(int y0, int x0,int y1,int x1) { // 2つのデータx, yが属する木が同じならtrueを返す
        int rx = root(y0,x0);
        int ry = root(y1,x1);
        return rx == ry;
    }
};
//座標圧縮
vector<ll> Ccomp(vector<ll> a){
    vector<ll> b = a;
    sort(b.begin(),b.end());
    b.erase(unique(b.begin(),b.end()),b.end());//ダブり消去
    vector<ll> rtn;
    rep(j,a.size()){
        ll pb = lower_bound(b.begin(),b.end(),a[j]) - b.begin();
        rtn.push_back(pb);
    }
    return rtn;
}
/// ここから////////////////////////////////////////////




using F = ll;
using S = ll;
string s;

ll modPow(ll a, ll n, ll mod) { if(mod==1) return 0;ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
void cincout(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(15);
}
//seg,遅延segの設定-----ここから
S op(S a,S b){return a + b;}//何を求めるか(最大値とか)

S e(){return 0;}//モノイド(初期値)

S bop(S a,S b){return a * b;};

S be(){return 1;}

ll v;

//bool f(ll a){return v > a;}//めんどいやつ

//S mapping (F a,S b){return a + b;}//遅延処理

F composition (F a,F b){return a + b;}//遅延中の枝にさらに処理

F id(){return 0;}//遅延のモノイド

vector<int> Op(vector<int> a,vector<int> b){a.insert(a.end(),b.begin(),b.end()); return a;}

vector<int> E(){return vector<int> (0);}

//segここまで
string abc = "abcdefghijklmnopqrstuvwxyz";
//string abc = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

ll mod = 998244353;
ll INF  =ll(2e18);
//かなしみ
int main() {
    cincout();
    cin >> n;
    vector2<pairs<ll>> a(n+1);
    for(int j = 2;j * j <= n;j++){
        if(a[j].size() == 0){
            for(int i = j;i <= n;i++){
                ll now = i;
                while(now % j == 0){
                    if(now == i)a[i].push_back({j,0});
                    a[i][a[i].size()-1].second++;
                    now /= j;
                }
            }
        }
    }
    for(int j = 2;j <= n;j++){
        ll now = 1;
        for(auto i : a[j]){
            now *= modPow(i.first,i.second,INF);
        }
        if(now != j)a[j].push_back({j / now,1});
    }
    vector<ll> b(n+1,0);
    ll bs = 1;
    ll bk = 0;
    for(int j = 2;j <= n;j++){
        for(auto i : a[j]){
            if(b[i.first] == 0)bk++;
            b[i.first] += i.second;
        }
    }

    for(int j = 2;j <= n;j++){
        if(b[j] != 0)bs *= (b[j]+1);
    }
    mint ans = 0;
    sort(b.begin(),b.end());
    vector<ll> d(n+2,1);
    for(int j : b){
        if(j == 0)continue;
        vector<ll> e(j+2,0);
        for(int i = 1;i <= j;i++){
            if(i == 0)e[n+1]++;
            else e[j / i]++;
        }
        ll sumnow = 1;
        for(int i = j;i >= 1;i--){
            e[i] += sumnow;
            sumnow += e[i] - sumnow;
        }
        ll now = 1;
        while(now <= j){
            //if(d[now] == 0)d[now] = e[now];
            d[now] *= e[now];
            now++;
        }
    }
    //for(int j = n-1;j >= 1;j--)d[j] += d[j + 1];
    ll minus = 0;
    for(int j = n;j >= 1;j--){
        //cout << d[j] << endl;
        ans += j * max(0LL,(d[j]-1) - minus);
        minus += (d[j]-1-minus);
    }
    cout << ans.val()  << endl;
    // return 0;
    // for(int j : b){
    //     if(j == 0)continue;
    //     else{
            
    //         bs /= (j+1);
    //         bk--;
    //         ll nowbs = bs;
    //         for(int k = 1;k <= j;k++){
    //             ans += nowbs * (j / k);
    //             nowbs-=bk;
    //         }
    //         cout << j << " " << ans.val() << endl;
    //         // cout << j << " " << bs * ((j * (j + 1)) / 2) << endl;;
    //         // ans += bs * ((j * (j + 1)) / 2);
    //     }
    // }
    // cout << ans.val() << endl;
    return 0;
}