1 const
  2     maxn=100100;
  3     h=1<<31;
  4 type
  5     node=record
  6       n,m,a,id:longint;
  7     end;
  8 var
  9     q:array[0..maxn]of node;
 10     flag:array[0..maxn]of boolean;
 11     p,u,k,f,ans,c:array[0..maxn]of longint;
 12     t,tot,max:longint;
 13
 14 function min(x,y:longint):longint;
 15 begin
 16     if x<y then exit(x);
 17     exit(y);
 18 end;
 19
 20 procedure swap(var x,y:longint);
 21 var
 22     t:longint;
 23 begin
 24     t:=x;x:=y;y:=t;
 25 end;
 26
 27 procedure swap(var x,y:node);
 28 var
 29     t:node;
 30 begin
 31     t:=x;x:=y;y:=t;
 32 end;
 33
 34 procedure sort(l,r:longint);
 35 var
 36     i,j:longint;
 37     y:int64;
 38 begin
 39     i:=l;
 40     j:=r;
 41     y:=f[k[(l+r)>>1]];
 42     repeat
 43       while f[k[i]]<y do
 44         inc(i);
 45       while f[k[j]]>y do
 46         dec(j);
 47       if i<=j then
 48       begin
 49         swap(k[i],k[j]);
 50         inc(i);
 51         dec(j);
 52       end;
 53     until i>j;
 54     if i<r then sort(i,r);
 55     if j>l then sort(l,j);
 56 end;
 57
 58 procedure pre;
 59 var
 60     i,j,s:longint;
 61 begin
 62     f[1]:=1;
 63     u[1]:=1;
 64     for i:=2 to max do
 65       begin
 66         if flag[i]=false then
 67         begin
 68           inc(tot);
 69           p[tot]:=i;
 70           f[i]:=i+1;
 71           u[i]:=-1;
 72         end;
 73         for j:=1 to tot do
 74           begin
 75             if int64(i)*p[j]>max then break;
 76             flag[i*p[j]]:=true;
 77             if i mod p[j]=0 then
 78               begin
 79                 s:=p[j];
 80                 while i mod (int64(s)*p[j])=0 do
 81                   s:=s*p[j];
 82                 if s=i then f[i*p[j]]:=(s*p[j]*p[j]-1)div(p[j]-1)
 83                 else f[i*p[j]]:=f[i div s]*f[s*p[j]];
 84                 break;
 85               end
 86             else
 87               begin
 88                 f[i*p[j]]:=f[i]*(p[j]+1);
 89                 u[i*p[j]]:=-u[i];
 90               end;
 91           end;
 92       end;
 93     for i:=1 to max do
 94       k[i]:=i;
 95     sort(1,max);
 96 end;
 97
 98 procedure sort2(l,r:longint);
 99 var
100     i,j,y:longint;
101 begin
102     i:=l;
103     j:=r;
104     y:=q[(l+r)>>1].a;
105     repeat
106       while q[i].a<y do
107         inc(i);
108       while q[j].a>y do
109         dec(j);
110       if i<=j then
111       begin
112         swap(q[i],q[j]);
113         inc(i);
114         dec(j);
115       end;
116     until i>j;
117     if i<r then sort2(i,r);
118     if j>l then sort2(l,j);
119 end;
120
121 procedure init;
122 var
123     i:longint;
124 begin
125     read(t);
126     for i:=1 to t do
127       begin
128         read(q[i].n,q[i].m,q[i].a);
129         q[i].id:=i;
130         if q[i].n>q[i].m then swap(q[i].n,q[i].m);
131         if max<q[i].n then max:=q[i].n;
132       end;
133     sort2(1,t);
134 end;
135
136 procedure add(x,y:longint);
137 begin
138     while x<=100000 do
139       begin
140         c[x]:=longint(int64(c[x])+y);
141         x:=x+(x and (-x));
142       end;
143 end;
144
145 function sum(x:longint):longint;
146 begin
147     sum:=0;
148     while x>0 do
149       begin
150         sum:=longint(int64(sum)+c[x]);
151         x:=x-(x and (-x));
152       end;
153 end;
154
155 procedure main;
156 var
157     i,j,kk,s,lasta,s1,s2:longint;
158 begin
159     lasta:=1;
160     for i:=1 to t do
161       begin
162         while (lasta<=max) and (f[k[lasta]]<=q[i].a) do
163           begin
164             s:=k[lasta];
165             j:=1;
166             while s<=max do
167               begin
168                 if u[j]<>0 then add(s,f[k[lasta]]*u[j]);
169                 inc(s,k[lasta]);
170                 inc(j);
171               end;
172             inc(lasta);
173           end;
174         kk:=1;
175         while kk<=q[i].n do
176           begin
177             s1:=q[i].n div kk;
178             s2:=q[i].m div kk;
179             s:=min(trunc(q[i].n/s1),trunc(q[i].m/s2));
180             ans[q[i].id]:=longint(int64(ans[q[i].id])+int64(longint(int64(s1)*s2))*longint(int64(sum(s))-sum(kk-1)));
181             kk:=s+1;
182           end;
183       end;
184     for i:=1 to t do
185       if ans[i]<0 then writeln(ans[i]+h)
186       else writeln(ans[i]);
187 end;
188
189 begin
190     init;
191     pre;
192     main;
193 end.