Basic Maths

I
```"""Implementation of Basic Math in Python."""

import math

def prime_factors(n: int) -> list:
"""Find Prime Factors.
>>> prime_factors(100)
[2, 2, 5, 5]
>>> prime_factors(0)
Traceback (most recent call last):
...
ValueError: Only positive integers have prime factors
>>> prime_factors(-10)
Traceback (most recent call last):
...
ValueError: Only positive integers have prime factors
"""
if n <= 0:
raise ValueError("Only positive integers have prime factors")
pf = []
while n % 2 == 0:
pf.append(2)
n = int(n / 2)
for i in range(3, int(math.sqrt(n)) + 1, 2):
while n % i == 0:
pf.append(i)
n = int(n / i)
if n > 2:
pf.append(n)
return pf

def number_of_divisors(n: int) -> int:
"""Calculate Number of Divisors of an Integer.
>>> number_of_divisors(100)
9
>>> number_of_divisors(0)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
>>> number_of_divisors(-10)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
"""
if n <= 0:
raise ValueError("Only positive numbers are accepted")
div = 1
temp = 1
while n % 2 == 0:
temp += 1
n = int(n / 2)
div *= temp
for i in range(3, int(math.sqrt(n)) + 1, 2):
temp = 1
while n % i == 0:
temp += 1
n = int(n / i)
div *= temp
if n > 1:
div *= 2
return div

def sum_of_divisors(n: int) -> int:
"""Calculate Sum of Divisors.
>>> sum_of_divisors(100)
217
>>> sum_of_divisors(0)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
>>> sum_of_divisors(-10)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
"""
if n <= 0:
raise ValueError("Only positive numbers are accepted")
s = 1
temp = 1
while n % 2 == 0:
temp += 1
n = int(n / 2)
if temp > 1:
s *= (2**temp - 1) / (2 - 1)
for i in range(3, int(math.sqrt(n)) + 1, 2):
temp = 1
while n % i == 0:
temp += 1
n = int(n / i)
if temp > 1:
s *= (i**temp - 1) / (i - 1)
return int(s)

def euler_phi(n: int) -> int:
"""Calculate Euler's Phi Function.
>>> euler_phi(100)
40
>>> euler_phi(0)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
>>> euler_phi(-10)
Traceback (most recent call last):
...
ValueError: Only positive numbers are accepted
"""
if n <= 0:
raise ValueError("Only positive numbers are accepted")
s = n
for x in set(prime_factors(n)):
s *= (x - 1) / x
return int(s)

if __name__ == "__main__":
import doctest

doctest.testmod()
```