#include<bits/stdc++.h>
#define LL long long
#define fr(x) freopen(#x".in","r",stdin);freopen(#x".out","w",stdout);
using namespace std;
const int N=1e5+5;
int T,n,m,a,pr[N];LL S[N],mu[N];bool v[N];
inline void init(int M)
{
	for(int i=2;i<=M;i++)
	{
		if(!v[i]) pr[++pr[0]]=i,mu[i]=-1;
		for(int j=1;j<=pr[0]&&i*pr[j]<=M;j++)
		{
			v[i*pr[j]]=1;if(i%pr[j]==0) break;
			mu[i*pr[j]]=-mu[i];
		}
	}mu[1]=1;
	for(int i=1;i<=M;i++) mu[i]=mu[i-1]+1ll*mu[i]*i*i;
	for(int i=1;i<=M;i++) S[i]=S[i-1]+i;
}
inline LL f(int r,int a)
{
	LL ans=0;int u=min(r,a);
	for(int i=1,j;i<=u;i=j+1) j=r/(r/i),ans+=mu[r/i]*(S[min(j,u)]-S[i-1]);
	return ans;
}

int main()
{
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);cin>>T;init(N-5);
	while(T--)
	{
		cin>>n>>m>>a;if(n>m) swap(n,m);LL ans=0;
		for(int i=1,j;i<=n;i=j+1) j=min(n/(n/i),m/(m/i)),ans+=S[n/i]*S[m/i]*(f(j,a)-f(i-1,a));
		cout<<ans<<"\n";
	}
	return 0;
}