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import math

def primeFactors(n):

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 numberOfDivisors(n):

div = 1

temp = 1

while n % 2 == 0:

temp += 1

n = int(n / 2)

div = 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 = div * (temp)

return div

def sumOfDivisors(n):

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 s

def eulerPhi(n):

l = primeFactors(n)

l = set(l)

s = n

for x in l:

s *= (x - 1)/x

return s

def main():

print(primeFactors(100))

print(numberOfDivisors(100))

print(sumOfDivisors(100))

print(eulerPhi(100))

if __name__ == '__main__':

main()

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