Test for Exactly Three Positive Divisors
Company: Bloomberg
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
### Problem
Return whether the positive integer `n` has exactly three distinct positive divisors. A divisor divides `n` without remainder; count both 1 and `n` when they are distinct.
```cpp
class Solution {
public:
bool isThree(int n);
};
```
### Examples
**Example 1:**
```text
n = 9
Output: true
Explanation: The divisors are 1, 3, and 9.
```
**Example 2:**
```text
n = 16
Output: false
Explanation: The divisors are 1, 2, 4, 8, and 16.
```
### Constraints
- `1 <= n <= 10^4`.
### Clarifying Questions
Only positive divisors count; 1 has just one divisor.
```hint Inspect the structure
How can divisor pairs be counted without visiting all integers up to n?
```
### Reasoning checkpoints
- Establish the exact number of distinct positive divisors without double-counting any divisor.
- Handle `n=1` and account correctly for coinciding divisor-pair members.
### Optional extensions
Can you characterize all positive integers that have exactly three positive divisors?
Overview: Test for Exactly Three Positive Divisors. Given positive integer n, return whether exactly three positive integers divide it without remainder. Count 1 and n themselves as divisors.