def problem462():
    """


    A 3-smooth number is an integer which has no prime factor larger than 3.
       For an integer N, we define S(N) as the set of 3-smooth numbers less than
       or equal to N . For example, S(20) = { 1, 2, 3, 4, 6, 8, 9, 12, 16, 18 }.

       We define F(N) as the number of permutations of S(N) in which each element
       comes after all of its proper divisors.

       This is one of the possible permutations for N = 20.
       - 1, 2, 4, 3, 9, 8, 16, 6, 18, 12.
       This is not a valid permutation because 12 comes before its divisor 6.
       - 1, 2, 4, 3, 9, 8, 12, 16, 6, 18.

       We can verify that F(6) = 5, F(8) = 9, F(20) = 450 and F(1000) ≈
       8.8521816557e21.
       Find F(10^18). Give as your answer its scientific notation rounded to ten
       digits after the decimal point.
       When giving your answer, use a lowercase e to separate mantissa and
       exponent. E.g. if the answer is 112,233,445,566,778,899 then the answer
       format would be 1.1223344557e17.
    """
    pass
