defmodule AntiPrimes do
	def divcount(n) when is_integer(n), do: divcount(n, 1, 0)

	def divcount(n, d, count) when d * d > n, do: count
	def divcount(n, d, count) do
		divs = case rem(n, d) do
			0 ->
				case n - d * d do
					0 -> 1
					_ -> 2
				end
			_ -> 0
		end
		divcount(n, d + 1, count + divs)
	end

	def antiprimes(n), do: antiprimes(n, 1, 0, [])

	def antiprimes(0, _, _, l), do: Enum.reverse(l)
	def antiprimes(n, m, max, l) do
		count = divcount(m)
		case count > max do
			true -> antiprimes(n-1, m+1, count, [m|l])
			false -> antiprimes(n, m+1, max, l)
		end
	end

	def main() do
		:io.format("The first 20 anti-primes are ~w~n", [antiprimes(20)])
	end
end