#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <string>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long ll;
const int maxn = 5e5+10;
int mobi[maxn];
int preMobi[maxn][20];
int pricnt[maxn];
bool isPrime[maxn];
vector<int> prime;

void getMobi(){
    memset(isPrime,1,sizeof isPrime);
    memset(pricnt,0,sizeof pricnt);
    mobi[1] = 1;
    for(int i = 2; i < maxn; i++){
        if(isPrime[i]){
            mobi[i] = -1;
            pricnt[i] = 1;
            prime.push_back(i);
        }
        for(int j = 0; j < prime.size() && i*prime[j] < maxn; j++){
            pricnt[i*prime[j]] = pricnt[i]+1;
            isPrime[i*prime[j]] = false;
            if(i%prime[j]==0){
                mobi[i*prime[j]] = 0;
                break;
            }else{
                mobi[i*prime[j]] = -mobi[i];
            }
        }
    }
}
void getpreMobi(){
    memset(preMobi,0,sizeof preMobi);
    for(int i = 1; i < maxn; i++){
        for(int j = i; j < maxn; j += i){
            preMobi[j][pricnt[i]] += mobi[j/i];
        }
    }
    for(int i = 1; i < maxn; i++){
        for(int j = 0; j < 20; j++){
            preMobi[i][j] += preMobi[i-1][j];
        }
    }
    for(int i = 0; i < maxn; i++){
        for(int j = 1; j < 20; j++){
            preMobi[i][j] += preMobi[i][j-1];
        }
    }
}
int n,m,p;
ll ans;
void solve(){
    ans = 0;
    for(int i = 1; i <= n; i++){
        int ed = min(n/(n/i),m/(m/i));
        ans += ll(preMobi[ed][p]-preMobi[i-1][p])*(n/i)*(m/i);
        i = ed;
    }
    cout<<ans<<endl;

}
void init(){
    getMobi();
    getpreMobi();

}
int main(){
    init();
    int ncase;
    cin >> ncase;
    while(ncase--){
        scanf("%d%d%d",&n,&m,&p);
        if(p>=19){
            cout<<(ll)n*m<<endl;
            continue;
        }
        if(n > m) swap(n,m);
        solve();
    }
    return 0;
}