Contents

# coding: utf-8
class Integer
  # Algorithm derived from Formulas for pi(n) and the n-th prime by Sebastian
  # Martin Ruiz and Jonathan Sondow [arXiv:math/0210312v2 [math.NT]]

  # Returns the number of divisors of self
  def τ 
    # TODO: Consider something simpler, and perhaps faster, like
    # primaries.map(&:last).map(&:succ).reduce(:*)
    n = self
    return @nod if defined?(@nod)
    @nod = (1..isqrt).
      map {|i|  n.quo(i).to_i - (n - 1).quo(i).to_i }.
      reduce(:+) * 2
    @nod -= 1 if square?
    @nod
  end


  alias :number_of_divisors :τ 
  alias :d :τ 
end

Version data entries

2 entries across 2 versions & 1 rubygems

Version	Path
numb-0.152.0	lib/numb/number_of_divisors.rb
numb-0.138.0	lib/numb/number_of_divisors.rb