//#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define pi acos(-1.0)
#define ll long long
#define mod 1000000007
#define C 0.5772156649
#define ls l,m,rt<<1
#define rs m+1,r,rt<<1|1
#define pil pair<int,ll>
#define pii pair<int,int>
#define ull unsigned long long
#define base 1000000000000000000
#define fio ios::sync_with_stdio(false);cin.tie(0)using namespace std;const double g=10.0,eps=1e-12;
const int N=500000+10,maxn=400000+10,inf=0x3f3f3f3f;int mu[N],prime[N],sum[N][20];
bool mark[N];
int num[N];
void init()
{mu[1]=1;int cnt=0;for(int i=2;i<N;i++){if(!mark[i])prime[++cnt]=i,mu[i]=-1,num[i]=1;for(int j=1;j<=cnt;j++){int t=i*prime[j];if(t>N)break;mark[t]=1;num[t]=num[i]+1;if(i%prime[j]==0){mu[t]=0;break;}else mu[t]=-mu[i];}}for(int i=1;i<N;i++)for(int j=i;j<N;j+=i)sum[j][num[i]]+=mu[j/i];for(int i=1;i<N;i++)for(int j=1;j<19;j++)sum[i][j]+=sum[i][j-1];for(int i=1;i<N;i++)for(int j=0;j<19;j++)sum[i][j]+=sum[i-1][j];
}
int main()
{init();int t;scanf("%d",&t);while(t--){int n,m,p;scanf("%d%d%d",&n,&m,&p);if(p>18){printf("%lld\n",(ll)n*m);continue;}ll ans=0;for(int i=1,last;i<=min(n,m);i=last+1){last=min(n/(n/i),m/(m/i));ans+=(ll)(sum[last][p]-sum[i-1][p])*(n/i)*(m/i);}printf("%lld\n",ans);}return 0;
}
/****************************************/