euler-023

def sum_of_proper_divisors(number)
  divisors = [1]
  (2..Math.sqrt(number)).each do |i|
    if number % i == 0
      divisors << i
      divisors << number / i unless i == number / i
    end
  end
  divisors.sum
end

def is_abundant?(number)
  sum_of_proper_divisors(number) > number
end

limit = 28123
abundant_numbers = (1..limit).select { |num| is_abundant?(num) }

sums_of_two_abundants = Set.new
abundant_numbers.each do |a|
  abundant_numbers.each do |b|
    sum = a + b
    break if sum > limit
    sums_of_two_abundants.add(sum)
  end
end

non_abundant_sums = (1..limit).reject { |num| sums_of_two_abundants.include?(num) }

total_sum = non_abundant_sums.sum

puts "Sum of all numbers that cannot be written as the sum of two abundant numbers: #{total_sum}"