# -*- coding: utf-8 -*-
'''Problem 70
Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6.
The number 1 is considered to be relatively prime to every positive number, so φ(1)=1.
Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation of 79180.
Find the value of n, 1 < n < 107, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum.'''
from __future__ import division
from aritmetica import factoriza
from aritmetica import totient
from aritmetica import ndigitos
from aritmetica import digitos
import aritmetica
import time
Tt=time.time()
MIN=1.1
for n in xrange(2,10**7):
t = totient(n)
#print n, t
if (ndigitos(t) == ndigitos(n)) and (n/t<MIN) and (sorted(digitos(t))==sorted(digitos(n))):
print n, t, n/t
MIN=n/t
print "\n====\n", time.time()-Tt
from aritmetica import ndigitos
c=0
for a in xrange(1,50):
for b in xrange(1,50):
if ndigitos(pow(a,b))==b:
print (a,b, pow(a,b))
c=c+1
print "===\n",c
from fractions import Fraction
from aritmetica import ndigitos
def f(r):
return 1+1/(1+r)
a = Fraction(3,2)
c=0
for r in xrange(2,1001):
a = f(a)
if ndigitos(a.numerator)>ndigitos(a.denominator):
print a
c=c+1
print "-----\n",c
