github.com/captn3m0/codechef.git

---
languages_supported:
    - NA
title: PRDIVSUM
category: NA
old_version: true
problem_code: PRDIVSUM
tags:
    - NA
layout: problem
---
###  All submissions for this problem are available. 

For a given positive integer **N** find the number of all pairs **(a, b)** of positive integers such that **1 <= a < b <= N** and the sum **a + b** divides the product **a \* b**.

### Input

The first line contains a single positive integer **T <= 5**, the number of test cases. **T** test cases follow. The only line of each test case contains a positive integer **N <= 109**.

### Output

For each test case, output a single line containing the answer for the corresponding test case.

### Example

<pre><b>Input:</b>
2
2
15

<b>Output:</b>
0
4

</pre>### Explanation

In the second test case required pairs are (3, 6), (4, 12), (6, 12) and (10, 15).