euler-021

def sum_of_proper_divisors(number)
  return 0 if number == 1
  
  divisor_sum = 1  # 1 is always a proper divisor
  (2..Math.sqrt(number)).each do |potential_divisor|
    if number % potential_divisor == 0
      divisor_sum += potential_divisor
      divisor_sum += number / potential_divisor unless potential_divisor == Math.sqrt(number)
    end
  end
  
  divisor_sum
end

def are_amicable?(a, b)
  sum_of_proper_divisors(a) == b && sum_of_proper_divisors(b) == a && a != b
end

amicable_numbers = []

(1..9999).each do |number|
  potential_amicable_partner = sum_of_proper_divisors(number)
  
  if are_amicable?(number, potential_amicable_partner)
    amicable_numbers << number
  end
end

sum_of_amicable_numbers = amicable_numbers.sum

puts "The sum of all amicable numbers under 10000 is #{sum_of_amicable_numbers}"

#ran in 3.14s