Cod sursa(job #2616987)

Utilizator OvidRata Ovidiu Ovid Data 20 mai 2020 15:55:50
Problema Suma si numarul divizorilor Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 1.75 kb
#include<bits/stdc++.h>
using namespace std;
#define INIT  ios_base :: sync_with_stdio(0); cin.tie(); cout.tie();mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define mp make_pair
#define pb push_back
#define ft first
#define sc second
#define ll long long
#define pii pair<int, int>
#define MOD 9973
#define int ll
#define cin fin
#define cout fout
ifstream fin("ssnd.in"); ofstream fout("ssnd.out");

vector<int> p;


int fi;

int exp(int x, int e){


if(e==0){return 1;}

if(e%2==0){
    return (exp( (x*x)%MOD , e/2))%MOD;
}
else{
    return (x* (exp( (x*x)%MOD, e/2)%MOD )   )%MOD;
}



}




int phi(int n){
int res=n;
int x=n;

for(int i=2; i<=sqrt(x); i++){

    if(res%i==0){
        res-=res/i;
        while(x%i==0){
            x/=i;
        }
    }




}

if(n>1){
    res-=res/n;
}

return res;
}




int invers(int n){


return (exp(n, fi-1))%MOD;

}








int32_t main(){
INIT
int t;
cin>>t;

fi=phi(MOD);
vector<bool> sv; sv.assign(1000010, false);

for(int i=2; i<=1000; i++){

    if(!sv[i]){
        for(int j=i*i; j<=1000000; j+=i){
            sv[j]=true;
        }
    }


}

for(int i=2; i<=1000000; i++){
    if(!sv[i]){
        p.pb(i);
    }
}



for(;t;t--){
    int n;
    cin>>n;
    int nr=1, sum=1;

    for(int i=0; p[i]<=sqrt(n); i++){
        if(n%p[i]==0){
                int d=0;
            while(n%p[i]==0){
                n/=p[i]; d++;
            }

            nr*=(d+1)%MOD; nr%=MOD;  sum*=(exp(p[i], d+1)-1  )%MOD; sum%=MOD; sum*=invers(p[i]-1)%MOD; sum%=MOD;
        }
    }

    if(n>1){
        nr*=2; sum*=(n+1)%MOD; sum%=MOD; nr%=MOD;
    }
cout<<nr<<" "<<sum<<"\n";
}



return 0;
}