Sure, I can help you write a test case generator for the given problem statement of Euler's Phi function.

Here's a suitable test case generator function for this problem:

```python
import random

def tcgen():
    n = random.randint(1, 10**9)
    return n

# Example usage
if __name__ == "__main__":
    n = tcgen()
    print(n)
```

This function generates a random integer `n` within the specified range (1 ≤ n ≤ 1000000000) and returns it. When the function is executed, it will print a random value of `n` which can be used as an input for the Euler's Phi function problem.

If you need more test cases at once, you can modify the function slightly to generate multiple test cases:

```python
def multiple_tcgen(num_cases):
    test_cases = [random.randint(1, 10**9) for _ in range(num_cases)]
    return test_cases

# Example usage
if __name__ == "__main__":
    num_cases = 10  # Specify the number of test cases you want to generate
    test_cases = multiple_tcgen(num_cases)
    for tc in test_cases:
        print(tc)
```

This function `multiple_tcgen` will generate a list of random test cases and print each of them. You can adjust the `num_cases` variable to specify how many test cases you want to generate.

These generators provide the input `n` within the required constraints and can be used to create a variety of test cases for the Euler's Phi function problem.