Sum Amicable Numbers

Write a Python function `sum_amicable_numbers(limit)` that calculates the sum of all amicable numbers from 1 to a given limit (inclusive). Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number.

#### Example Usage
```python [main.nopy]
print(sum_amicable_numbers(300))  # Output: 504
print(sum_amicable_numbers(10000))  # Output: 31626
```

#### Constraints
- The input `limit` will be a positive integer.
- Proper divisors of a number are all divisors excluding the number itself.
def sum_amicable_numbers(limit):
    """
    Calculate the sum of all amicable numbers from 1 to the given limit.

    Args:
        limit (int): The upper limit to find amicable numbers.

    Returns:
        int: The sum of all amicable numbers up to the limit.
    """
    # Placeholder for the solution
    pass
Advanced functionsloopsconditionalsmath
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