Problem p02470 - Generation 1

Orig Description

Euler's Phi Function
For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n.
Input
n
An integer n (1 ≤ n ≤ 1000000000).
Output
The number of totatives in a line.
Sample Input 1
6
Sample Output 1
2
Sample Input 2
1000000
Sample Output 2
400000

Extracted Specification

An integer n (1 ≤ n ≤ 1000000000).

### Example Input:

```
6
```

### Function Signature:
Write a function f(n) that takes in the input.
def f(n: int):
    '''
    n: an integer
    '''

Test Case Generator

Sure, I'll write a test case generator for the Euler's Phi Function problem.

### Test Case Generator for Euler's Phi Function

Here's a Python function that generates random test cases for the Euler's Phi Function problem.

```python
import random

def tcgen():
    n = random.randint(1, 1000000000)
    return n

# Example usage:
random_test_case = tcgen()
print(random_test_case)
```

### Explanation

1. **Function `tcgen`**:
   - Generates a random integer `n` within the range `[1, 1000000000]`.
   - Returns the integer `n`.

This function can be used to generate numerous random test cases to test the algorithm that calculates the Euler's Phi Function.

### Note:

- Since calculating the Euler's Phi Function for large numbers might be computationally intensive, ensure that your algorithm is efficient.
- You can use known libraries like `sympy` in Python, which has an implementation for Euler's Totient function, to verify the correctness of the output for generated test cases.

Example using `sympy` to verify a generated test case:

```python
from sympy import totient

# Generate a random test case
n = tcgen()

# Calculate the Euler's Phi Function for n
phi_n = totient(n)
print(f"Test case: {n}")
print(f"Output: {phi_n}")
```

This approach helps ensure that the test cases are valid and provides a mechanism to verify the correctness of your algorithm.

Extract Arguments

def extract_arguments(fh):
    n = int(fh.readline().strip())
    return n