# -*- 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