Sure, I can help you write a test case generator for the given problem statement "Problem D: Numbers". Below is the Python code for the test case generator:

```python
import random

def tcgen():
    # Generate a random value for n within the given constraints
    n = random.randint(1, 1500)
    return n

# Example usage
n = tcgen()
print(n)
```

This function will generate a random value for \( n \) within the given constraints \( 1 \leq n \leq 1500 \). To generate and format the test cases for this problem, we will need to generate the smallest of \( n \) consecutive positive integers and their divisors.

Here's an example of how you can generate valid test cases for this problem:

```python
def generate_divisors(x):
    """ Return a list of divisors of x excluding 1 and x. """
    divisors = []
    for i in range(2, int(x**0.5) + 1):
        if x % i == 0:
            divisors.append(i)
            if i != x // i:
                divisors.append(x // i)
    return divisors

def generate_test_case(n):
    smallest_x = random.randint(2, 10**6)  # Generate a random starting point (reasonably large to avoid trivial cases)
    consecutive_numbers = [smallest_x + i for i in range(n)]
    
    # Collect divisors for each number
    divisors_list = [generate_divisors(num) for num in consecutive_numbers]

    # Ensure each number has at least one non-trivial divisor
    for i in range(len(divisors_list)):
        if not divisors_list[i]:
            divisors_list[i] = [smallest_x + i]
    
    return smallest_x, consecutive_numbers, divisors_list

def tcgen():
    n = random.randint(1, 1500)
    smallest_x, consecutive_numbers, divisors_list = generate_test_case(n)
    
    return n, smallest_x, consecutive_numbers, divisors_list

# Example usage
n, smallest_x, consecutive_numbers, divisors_list = tcgen()
print(n)
print(smallest_x)
for i in range(n):
    print(consecutive_numbers[i])
    print(divisors_list[i])
```

### Explanation:
1. **`generate_divisors`**: A helper function to get divisors of a number excluding 1 and itself.
2. **`generate_test_case`**: This generates a list of \( n \) consecutive numbers starting from a random number `smallest_x` and ensures each number has at least one non-trivial divisor. If a number has no divisors other than 1 and itself, the number itself is added as its divisor.
3. **`tcgen`**: Generates the value for \( n \) and then calls `generate_test_case` to produce the smallest number, the consecutive numbers, and their divisors.

Using this generator, you can produce valid test cases for the given problem statement. The example usage shows how to generate and print a test case. Adjusting the `smallest_x` random range can help to control the size of the numbers generated.