Sure, I can help you write a test case generator for the given problem statement "Twice of oneself." The generator will create random test cases within the specified constraints. Here is the implementation in Python:

```python
import random

def generate_test_case():
    Q = random.randint(1, 10**5)  # Number of queries
    queries = [random.randint(2, 10**5) for _ in range(Q)]
    return Q, queries

def format_test_case(Q, queries):
    result = [str(Q)]
    result.extend(map(str, queries))
    return '\n'.join(result)

# Example usage to generate and print a test case
Q, queries = generate_test_case()
test_case = format_test_case(Q, queries)
print(test_case)
```

### Explanation:
1. **generate_test_case Function:**
   - **Q**: Randomly generates the number of queries between 1 and \(10^5\).
   - **queries**: Generates a list of \(Q\) integers, each ranging from 2 to \(10^5\).

2. **format_test_case Function:**
   - Converts the generated test case into the required input format as a string.
   - The first line contains the number of queries \(Q\).
   - The subsequent lines contain the \(Q\) integers.

### Example Output:
Running the example usage will print a test case, for instance:
```
5
25784
128
99999
2
45000
```

This output is consistent with the input format specified in the problem statement. You can use this generator to create multiple test cases for thorough testing of your solution.