CSP-S 2023 T17

#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;

long long solve1(int n) {
    vector<bool> p(n + 1, true);
    vector<long long> f(n + 1, 0), g(n + 1, 0);
    f[1] = 1;
    for (int i = 2; i * i <= n; i++) {
        if (p[i]) {
            vector<int> d;
            for (int k = i; k <= n; k *= i) d.push_back(k);
            reverse(d.begin(), d.end());
            for (int k : d) {
                for (int j = k; j <= n; j += k) {
                    if (p[j]) {
                        p[j] = false;
                        f[j] = i;
                        g[j] = k;
                    }
                }
            }
        }
    }
    for (int i = sqrt(n) + 1; i <= n; i++) {
        if (p[i]) {
            f[i] = i;
            g[i] = i;
        }
    }
    long long sum = 1;
    for (int i = 2; i <= n; i++) {
        f[i] = f[i / g[i]] * (g[i] * f[i] - 1) / (f[i] - 1);
        sum += f[i];
    }
    return sum;
}

long long solve2(int n) {
    long long sum = 0;
    for (int i = 1; i <= n; i++) {
        sum += i * (n / i);
    }
    return sum;
}

int main() {
    int n;
    cin >> n;
    cout << solve1(n) << endl;
    cout << solve2(n) << endl;
    return 0;
}