This program can tell if a number is perfect, abundant or deficient according to the Greek mathematician Nicomachus's classification scheme. This algorithm is fast, but its speed pales in comparison to the algorithm I wrote that uses ruby's Prime class.

perfect_numbers.rb

require 'benchmark'

class PerfectNumber
  def self.classify(number)
    raise RuntimeError if number <= 1
    sum_of_divisors = add_divisors(number)

    return 'deficient' if sum_of_divisors < number
    return 'abundant' if sum_of_divisors > number
    'perfect'
  end

  def self.add_divisors(number)
    sqrt_of_number = Math.sqrt(number)
    range = 2..sqrt_of_number.floor
    sum_of_divisors = 1

    range.each do |divisor_candidate|
      next unless number % divisor_candidate == 0
      sum_of_divisors += divisor_candidate
      sum_of_divisors +=
        number / divisor_candidate unless divisor_candidate == sqrt_of_number
    end

    sum_of_divisors
  end
  private_class_method :add_divisors
end

time = Benchmark.measure do
  PerfectNumber.classify(999_999_999_999_999_999)
end

p time # => #<Benchmark::Tms:0x007fab228bfb58 @label="", @real=64.7947408069158, @cstime=0.0, @cutime=0.0, @stime=0.05, @utime=64.69999999999999, @total=64.74999999999999>