PyPE solution to PE problem 69

    ProjectEuler.net problem 69
    ===========================

    Euler's Totient function, f(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, f(9)=6.

        n Relatively Prime f(n) n/f(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/f(n) for n = 10.

    Find the value of n = 1,000,000 for which n/f(n) is a maximum.

    Solution
    --------

    In order to maximize n/f(n), we want to minimize f(n). We note that if n is
    a multiple of 2, then every other number below it will be coprime. Further,
    we note that if n is a multiple of 3, then every /third/ number below it
    will be coprime. This continues for the sequence of primes.

    So, to obtain our answer, we begin with a set containing all possible values
    of n, then iterate through the prime numbers, removing all multiples of
    each prime number from the set until the length of the set reaches 1.

    Answer
    ------

    510510