divisors.rb

   1 load 'primes.rb'
   2
   3
   4 class Integer
   5   # Returns a Hash of prime factors of self.
   6   # Each key is a prime factor of self, and factors[i] is the power of that prime factor
   7   # For example 45.prime_factors # => {3 => 2, 5 => 1}
   8   #   or, 45 = 3 ** 2 * 5 ** 1
   9   def prime_factors
  10     primes = Primes.instance
  11     n = self
  12     factors = Hash.new(0)
  13     i = 0
  14     while n > 1
  15       if n % primes[i] == 0
  16         factors[primes[i]] += 1
  17         n = n.div primes[i]
  18       else
  19         i += 1
  20       end
  21     end
  22     factors
  23   end
  24
  25   def number_of_divisors
  26     factors = prime_factors
  27     factors.keys.reduce(1) {|a, factor| a *= factors[factor] + 1}
  28   end
  29
  30   def sum_of_divisors
  31     factors = prime_factors
  32     factors.keys.map {|f|
  33       (0..factors[f]).map {|a| f ** a}.reduce(:+)
  34       }.reduce(:*)
  35   end
  36
  37   def sum_of_proper_divisors
  38     sum_of_divisors - self
  39   end
  40
  41   def perfect?
  42     sum_of_proper_divisors == self
  43   end
  44
  45   def abundant?
  46     sum_of_proper_divisors > self
  47   end
  48
  49   def deficient?
  50     sum_of_proper_divisors < self
  51   end
  52
  53 end