Cod sursa(job #1911853)

Utilizator FredyLup Lucia Fredy Data 7 martie 2017 22:01:17
Problema Suma si numarul divizorilor Scor 100
Compilator cpp Status done
Runda Arhiva educationala Marime 1.54 kb
#include <fstream>
#include <bitset>
/// formula:
/// n = p1^d1 * p2^d2 * ... * pk^dk
/// nr div lui n = (d1+1) * (d2+1) * ... * (dk+1)
/// suma div lui n = (p1^(d1+1)-1)/(p1-1) * (p2^(d2+1)-1)/(p2-1) * ... * (pk^(dk+1)-1)/(pk-1)


using namespace std;

const int MAX_N = 1000005;
const int MOD = 9973;

ifstream fin ("ssnd.in");
ofstream fout ("ssnd.out");

long long N;
int T, K, P[MAX_N];
bitset <MAX_N> viz;

void ciur()
{
    for(int i = 2; i < MAX_N; ++i)
    {
        if(viz[i] == 0)
        {
            P[++K] = i;

            for(int j = i+i; j < MAX_N; j += i)
                viz[j] = 1;

        }
    }
}

inline int pow(int x, int p)
{
    int rez = 1;
    x %= MOD;

    for(; p; p >>= 1)
    {
        if(p & 1)
        {
            rez *= x;
            rez %= MOD;
        }

        x *= x;
        x %= MOD;
    }

    return rez;
}

void solve()
{
    fin >> N;

    int nd = 1, sd = 1;

    for(int i = 1; i <= K && 1LL * P[i] * P[i] <= N; ++i)
    {
        if(N % P[i]) continue;
        int p = 0;

        while(N % P[i] == 0)
        {
            N /= P[i];
            ++p;
        }

        nd *= (p+1);

        int p1 = (pow(P[i], p+1) - 1) % MOD;
        int p2 = pow(P[i]-1, MOD-2) % MOD;

        sd = (((sd * p1) % MOD) * p2) % MOD;
    }

    if(N > 1)
    {
        nd *= 2;
        sd = (1LL*sd*(N+1) % MOD);
    }

    fout << nd << " " << sd << "\n";
}



int main()
{
    ciur();

    for(fin >> T; T; --T)
        solve();

}