add solution for problem 23

problems/23/solution.exs

@@ -0,0 +1,38 @@
+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()
+