Project Euler problem69

class P69

  MAXN = 1000000
  def initialize(n = MAXN)
    @n = n
  end

  def main
    phis = phis( @n )
    phis.index( max_phi( phis ) ) + 1
  end
  
  def max_phi( phis )
    phis.inject do |max,phi|
      max < phi ? phi : max
    end
  end

  def phis( k )
    (1..k).map do |n|
      n/phi(n).to_f
    end
  end

  def phi(n)
    n.downto(1).select do |i|
      n.gcd(i) == 1
    end.size
  end
end