This module can tell if a number is perfect, abundant or deficient according to the Greek mathematician Nicomachus's classification scheme. The algorithm is fast.

perfect_numbers.rb

require 'prime'

module PerfectNumber
  def self.classify(number)
    raise "Number must be greater than or equal to two" if number < 2
    aliquot_sum = generate_aliquot_sum(number)

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

  def self.generate_aliquot_sum(number)
    primes, exponent_list = number.prime_division.transpose
    all_exponents = exponent_list.map { |exponent| (0..exponent).to_a }
    all_exponent_combinations = all_exponents.shift.product(*all_exponents)
    sum = 0

    all_exponent_combinations.each do |exponents|
      sum += divisor(primes, exponents)
    end

    sum -= number
  end

  def self.divisor(primes, exponents)
    primes.zip(exponents)
          .map { |prime, exponent| prime ** exponent }
          .reduce(:*)
  end
end