Solve the programming task below in a Python markdown code block.
Given an array A having N elements, Chef wonders how many pairs (i, j) exists such that 1 ≤ i < j ≤ N, and A_{i} \cdot A_{j} is divisible by i \cdot j. 

Can you help Chef in finding the number of such pairs?

------ Input Format ------ 

- The first line of input contains a single integer T, denoting the number of test cases. The description of the T testcases follows.
- The first line of each test case contains a single integer N denoting the number of elements in A.
- The second line of each test case contains N space separated integers A_{1}, A_{2},..., A_{N}.

------ Output Format ------ 

For each test case, print a single line containing one integer denoting the number of pairs that satisfies the above condition.

------ Constraints ------ 

$1 ≤ T ≤ 10^{4}$
$2 ≤ N ≤ 10^{5}$
$1 ≤ A_{i} ≤ 10^{5}$
- The sum of $N$ over all test cases does not exceed $10^{5}$

----- Sample Input 1 ------ 
3
3
1 2 3
4
2 3 5 6
5
3 9 14 6 10

----- Sample Output 1 ------ 
3
2
6

----- explanation 1 ------ 
Test Case $1$: For all possible pairs of $\{i, j\}$, $A_{i} \cdot A_{j}$ is divisible by $i \cdot j$.

Test Case $2$: The condition holds for the following two pairs of $\{i, j\}$: $\{1 , 2\}$, $\{1, 4\}$.