Sure! Let's write a test case generator for the given problem statement "Problem D: Numbers". We need to generate random values for \( n \) within the given constraints and then construct the output accordingly.

Here's the code for the test case generator:

```python
import random

def generate_consecutive_numbers(n):
    # Starting from a random number that ensures we don't exceed 5000 digits in output
    start = random.randint(1, 10**5)
    return [start + i for i in range(n)]

def generate_divisors(n):
    divisors = []
    numbers = generate_consecutive_numbers(n)
    
    for num in numbers:
        # Generate a divisor other than 1 and the number itself
        if num == 1:
            divisors.append(2)  # Since 1 only has itself as a divisor, we output 2 instead
        else:
            divisors.append(random.randint(2, num - 1))
    
    return numbers, divisors

def tcgen():
    n = random.randint(1, 1500)
    numbers, divisors = generate_divisors(n)
    
    return n, numbers, divisors

def format_output(n, numbers, divisors):
    output = [str(numbers[0])]
    output.extend(map(str, divisors))
    return "\n".join(output)

# Example usage:
n, numbers, divisors = tcgen()
print(n)
print(format_output(n, numbers, divisors))
```

### Explanation:
1. **generate_consecutive_numbers(n)**: Generates `n` consecutive numbers starting from a random integer within a reasonable range.
2. **generate_divisors(n)**: Generates a list of divisors such that each number in the list, except 1, has at least one divisor other than 1 and itself. We handle the special case for 1 by outputting 2 as its divisor.
3. **tcgen()**: Generates a random value for \( n \) within the specified range and then uses the helper functions to generate the numbers and their respective divisors.
4. **format_output(n, numbers, divisors)**: Formats the output in the required way, with the first line being the smallest number in the list, followed by the divisors of each consecutive number.

This should cover the generation of test cases as required by the problem statement.