Add the Integers Divisible by Three, Five, or Seven
Company: Amazon
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
### Problem
For a positive integer n, sum all integers from 1 through n inclusive that are divisible by at least one of 3, 5, or 7. Count a qualifying integer once even if several divisibility conditions hold.
```cpp
class Solution {
public:
int sumOfMultiples(int n);
};
```
### Examples
**Example 1:**
```text
Input: n = 5
Output: 8
Explanation: The qualifying integers are 3 and 5.
```
**Example 2:**
```text
Input: n = 15
Output: 81
Explanation: The qualifying integers are 3,5,6,7,9,10,12,14,15, whose sum is 81. Fifteen is counted once.
```
### Constraints
- `1 <= n <= 1000`.
### Clarifying Questions
- Is n included? Yes, when it qualifies.
- Must a value be divisible by all three numbers? No; any one is enough.
- Is a value divisible by several of them added several times? No; count it once.
- What if no integer qualifies? Return zero.
```hint Check the boundary
Check the value15, which satisfies more than one divisor condition.
```
Overview: Sum integers from 1 through n divisible by three, five or seven, counting each qualifying value only once.
