#include <cstdio>

#include <algorithm>

#include <cstring>

#define ll long long

#define setIO(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)

const long long mod = 2147483648;

const long long N = 100008;

const int maxn = 100009 ; 

using namespace std;

struct M{

    int delta;

    int id;

}opt[maxn];  

int prime[maxn],tot,vis[maxn],mu[maxn],g[maxn],answer[maxn];

int cmp2(M a,M b){ return a.delta < b.delta; }

void Init(){

    mu[1] = 1;

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

        if(!vis[i]) prime[++tot] = i, mu[i] = -1;

        for(int j=1;j <= tot && (ll)i * prime[j] <= N; ++j) {

            vis[i * prime[j]] = 1;

            if(i % prime[j]==0) {

                mu[i * prime[j]] = 0;

                break;

            }

            mu[i*prime[j]]=-mu[i];

        }

    }

    for(int i=1;i<maxn;++i)

        for(ll j=1;(ll)j*i<=N;++j) g[i*j] += i;

    for(int i=1;i<maxn;++i) opt[i].delta=g[i],opt[i].id=i;

    sort(opt+1,opt+maxn,cmp2);

}

struct BIT{

    ll C[maxn];

    int lowbit(int t) { return t & (-t); }

    void update(int x,ll k) {

        while(x < maxn) {

            C[x]+=k, C[x]%=mod;

            x+=lowbit(x);

        }

    }

    ll query(int x){

        ll sum=0;

        while(x>0) sum+=C[x],sum%=mod,x-=lowbit(x);

        return sum;

    }

}tree;

ll work(int n,int m,int p) {

    if(n>m) swap(n,m);

    long long sum=0;

    for(int i=1,j;i <= n;i=j+1) {

        j=min(n/(n/i),m/(m/i));

        sum+=(n/j)*(m/j)*(tree.query(j)-tree.query(i-1));

        sum%=mod;

    }

    return sum;

}

struct P{ int n,m,a,id; }node[maxn];

int cmp(P a,P b){ return a.a<b.a;  }

void oper(int p){ for(int i=1;i*opt[p].id<=N;++i) tree.update(opt[p].id*i,((ll)opt[p].delta*mu[i]+mod)%mod);  }

int main(){

    //setIO("input");

    Init();

    int T;

    scanf("%d",&T);

    for(int i=1;i<=T;++i) scanf("%d%d%d",&node[i].n,&node[i].m,&node[i].a),node[i].id=i;

    sort(node+1,node+1+T,cmp);

    int last=1;

    for(int i=1;i<=T;++i) {

        int j=last;

        while(opt[j].delta <= node[i].a) oper(j),++j;

        last=j;

        answer[node[i].id]=(int)work(node[i].n,node[i].m,node[i].a);

    }

    for(int i=1;i<=T;++i) printf("%d\n",(answer[i]+mod)%mod);

    return 0;

}