Certainly! Below is a test case generator for the given problem statement.

### Test Case Generator:

```python
import random

def tcgen():
    # Generate a random value for n within the given constraints
    n = random.randint(1, 10**6)
    
    return n

# Example usage:
# Generate a test case
n = tcgen()
print(n)
```

### Explanation:

This test case generator creates a random test case for the provided problem statement:

1. **n**: Randomly generated integer between 1 and 10^6.

You can run this generator multiple times to create different test cases for the problem.

### Example Output from the Generator:

```plaintext
834057
```

This output corresponds to a single randomly generated test case with \( n \) as 834057. You can use this in your program to test the correctness and performance of your solution.