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p69.py
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p69.py
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# -*- coding: utf-8 -*-
"""
Created on Sun Mar 26 12:11:13 2017
@author: Refaia
"""
import time
def isPrime(n) :
if n <= 1 :
return False
if n <= 3 :
return True
if n % 2 == 0 or n % 3 == 0 :
return False
i = 5
while i * i <= n :
if n % i == 0 or n % (i + 2) == 0 :
return False
i += 6
return True
def primeFactors(n):
i = 2
factors = set()
while i * i <= n:
if n % i != 0:
i += 1
else:
n //= i
factors.add(i)
if n > 1:
factors.add(n)
return factors
def eulerTotient(n) :
result = n
for prime in primeFactors(n) :
result *= (1 - (1 / prime))
return int(result)
def main() :
delta = time.time()
maxResult = 3
nMax = 6
for n in range(10, 1000001) :
tmp = (n / eulerTotient(n))
if (maxResult) < tmp :
maxResult = tmp
nMax = n
delta = time.time() - delta
return maxResult, nMax, delta
print(main())