defmodule AmicableNumbers do
  def divisors(n) do
    [ 1 |
    (for i <- 2..floor(:math.sqrt(n))//1,
      j = div(n, i),
      j == n / i do
        if i !== j, do: [i,j], else: [i]
    end |> Enum.flat_map(&(&1))) ]
  end
end

defmodule Abundance do
  def is_abundant?(n) do
    cache = Process.get(:abundance, %{})

    case cache |> Map.get(n) do
      nil ->
        sum = AmicableNumbers.divisors(n) |> Enum.sum()
        is? = sum > n
        Process.put(:abundance, Map.put(cache, n, is?))
        is?
      is? -> is? 
    end
  end
end

# sum of all numbers that can be expressed as sum of two abundant numbers
sum = for n <- 1..28123,
  mid = div(n, 2),
  Enum.any?(1..mid, &(Abundance.is_abundant?(&1) and Abundance.is_abundant?(n - &1))),
  reduce: 0
  do
    s -> s + n
end

(((28123*28124)/2) - sum)
|> IO.puts()