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