Implementation of Basic Math in Python. import math def primefactorsn: int  list: if n  0: raise ValueErrorOnly positive integers have prime factors pf   while n  2  0: pf.append2 n  intn  2 for i in range3, intmath.sqrtn  1, 2: while n  i  0: pf.appendi n  intn  i if n  2: pf.appendn return pf def numberofdivisorsn: int  int: if n  0: raise ValueErrorOnly positive numbers are accepted div  1 temp  1 while n  2  0: temp  1 n  intn  2 div  temp for i in range3, intmath.sqrtn  1, 2: temp  1 while n  i  0: temp  1 n  intn  i div  temp if n  1: div  2 return div def sumofdivisorsn: int  int: if n  0: raise ValueErrorOnly positive numbers are accepted s  1 temp  1 while n  2  0: temp  1 n  intn  2 if temp  1: s  2temp  1  2  1 for i in range3, intmath.sqrtn  1, 2: temp  1 while n  i  0: temp  1 n  intn  i if temp  1: s  itemp  1  i  1 return ints def eulerphin: int  int: if n  0: raise ValueErrorOnly positive numbers are accepted s  n for x in setprimefactorsn: s  x  1  x return ints if name  main: import doctest doctest.testmod
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()
