069.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

#Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than 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.
#n 	Relatively Prime 	φ(n) 	n/φ(n)
#2 	1 	1 	2
#3 	1,2 	2 	1.5
#4 	1,3 	2 	2
#5 	1,2,3,4 	4 	1.25
#6 	1,5 	2 	3
#7 	1,2,3,4,5,6 	6 	1.1666...
#8 	1,3,5,7 	4 	2
#9 	1,2,4,5,7,8 	6 	1.5
#10 	1,3,7,9 	4 	2.5

#It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10.

#Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.

#Answer:
	#510510

from time import time; t=time()
from mathplus import get_primes_by_sieve

M = 1000000
primes, sieves = get_primes_by_sieve(100)
s = 1
for p in primes:
    s *= p
    if s > M:
        s //= p
        break
print(s)#, time()-t