Counting Pairs Problem Statement

Given a positive integer N, determine the count of all possible positive integral pairs (X, Y) that satisfy the equation 1/X + 1/Y = 1/N.

Example:

Input:

T = 1
N = 2

Output:

3

Explanation:

The solutions for 1/X + 1/Y = 1/2 are (3, 6), (6, 3), (4, 4). Total count is 3.

Constraints:

• 1 ≤ T ≤ 100
• 1 ≤ N ≤ 104
• Time Limit: 1 sec.

Input Format:

The first line contains an integer 'T' which represents the number of test cases.
Each test case consists of a single positive integer 'N'.

Output Format:

Each test case output should be an integer denoting the count of the pairs satisfying the equation.
Print the result for each test case on a new line.

Note:

Implement the function to determine the count of pairs. No need to handle input/output formatting manually.