[Solution] Good Pairs CodeChef Solution | Solution CodeChef

Problem

You are given an array $A$ of length $N$.

A pair $(i, j)$ $(1\le i\lt j \le N)$ is said to be good if $gcd(A_i, A_j) = lcm(A_i, A_j)$. Here $gcd$ denotes the greatest common divisor and $lcm$ denotes least common multiple.

Find the total number of good pairs present in the given array.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• The first line of each test case contains an integer $N$ - the length of the array $A$.
• The second line of each test case contains $N$ space-separated integers $A_1,A_2,\ldots,A_N$.

Output Format

For each test case, output on a new line the total number of such good pairs possible in the given array.

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Explanation:

Test case $1$: No good pair is present.

Test case $2$: The good pairs $(i, j)$ are: $(2, 3), (3, 4),$ and $(2, 4)$. To elaborate, $gcd(A_2, A_3) = lcm(A_2, A_3) = 5$.

Test case $3$: The good pairs $(i, j)$ are: $(1, 4), (2, 3), (5, 6), (6, 7),$ and $(5, 7)$. To elaborate, $gcd(A_1, A_4) = lcm(A_1, A_4) = 2$.

Test case $4$: The good pair $(i, j)$ are: $(1, 2),$ and $(3, 4)$. To elaborate, $gcd(A_3, A_4) = lcm(A_3, A_4) = 18$.

Test case $5$: No good pair is present.