21.rb

require_relative 'lib/helper'

# Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
# If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.

# For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

# Evaluate the sum of all the amicable numbers under 10000.

def sum_proper_divisors(n)
  proper_divisors(n).reduce(&:+)
end

def simple
  sum = 0

  (2..9999).each do |n|
    other_half = sum_proper_divisors(n)
    next if other_half == n
    next unless n == sum_proper_divisors(other_half)
    sum += n
  end

  sum
end

run do
  simple
end