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basic_maths.py
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80 lines (70 loc) · 1.72 KB
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"""Implementation of Basic Math in Python."""
import math
def prime_factors(n: int) -> list:
"""Find Prime Factors.
>>> prime_factors(100)
[2, 2, 5, 5]
"""
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
"""
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
return div
def sum_of_divisors(n: int) -> int:
"""Calculate Sum of Divisors.
>>> sum_of_divisors(100)
217
"""
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
"""
s = n
for x in set(prime_factors(n)):
s *= (x - 1) / x
return int(s)
if __name__ == "__main__":
print(prime_factors(100))
print(number_of_divisors(100))
print(sum_of_divisors(100))
print(euler_phi(100))