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1236 - Pairs Forming LCM
  PDF (English) Statistics Forum
Time Limit: 2 second(s) Memory Limit: 32 MB

Find the result of the following code:

long long pairsFormLCM( int n ) {
    
long long res = 0;
    
for( int i = 1; i <= n; i++ )
        
for( int j = i; j <= n; j++ )
           
if( lcm(i, j) == n ) res++; // lcm means least common multiple
    
return res;
}

A straight forward implementation of the code may time out. If you analyze the code, you will find that the code actually counts the number of pairs (i, j) for which lcm(i, j) = n and (i ≤ j).

Input

Input starts with an integer T (≤ 200), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 1014).

Output

For each case, print the case number and the value returned by the function 'pairsFormLCM(n)'.

Sample Input

Output for Sample Input

15

2

3

4

6

8

10

12

15

18

20

21

24

25

27

29

Case 1: 2

Case 2: 2

Case 3: 3

Case 4: 5

Case 5: 4

Case 6: 5

Case 7: 8

Case 8: 5

Case 9: 8

Case 10: 8

Case 11: 5

Case 12: 11

Case 13: 3

Case 14: 4

Case 15: 2

 


Problem Setter: Jane Alam Jan
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