Find the value of n, 1 < n < 10^7, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum.
'''
def EulerProduct(n,factors):
# http://en.wikipedia.org/wiki/Euler's_totient_function
product = n
for i in set(factors):
product *= (1-1/i)
return product
n_limit = 100
# primes = sieve_for_primes_to(n_limit)
# print(len(primes))
print(list(enumerate(sieve_for_primes_to(n_limit))))
print([i*2+1 for i, v in enumerate(sieve_for_primes_to(n_limit)) if v and i>0])
# print(len([2] + [i*2+1 for i, v in enumerate(sieve_for_primes_to(10000000)) if v and i>0]))
# print(primes)
print("done")
# primes = set()
# min_ratio = float("Inf")
# min_n = 0
# min_phi = 0
# for n in range(2,n_limit+1):
# factors = prime_factors(n)
# if len(factors)==2:
# phi = int(EulerProduct(n,prime_factors(n)))
# if sorted(str(n)) == sorted(str(phi)):
# ratio = n/phi
factors = []
d = 2
while n > 1:
while n % d == 0:
factors.append(d)
n /= d
d = d + 1
if d*d > n:
if n > 1: factors.append(n)
break
return factors
total = 0
limit = 100000
primes = {2} | {i*2+1 for i, v in enumerate(sieve_for_primes_to(limit)) if v and i>0}
start = time.time()
for n in range(2,limit+1):
if n in primes:
total += n-1
else:
factors = {i for i in primes if n%i==0 and i<=n*0.5}
phi = int(EulerProduct(n,factors))
total += phi
if n%10000==0:
print(n,time.time()-start)
start = time.time()