Prime factors tree

prime_factors.hs

import Data.List (nub)
import Control.Monad
import System.Environment



main = getArgs >>= compressedFactors . read . head . (++["20"])

-- | Reduce the number of factors needed to create a number
compressedFactors m = do
  putStrLn "digraph G {"
  putStrLn "graph [pad=\"0.5\", nodesep=\"0\", ranksep=\"2\"];"
  mapM_ printTree [1..m::Int]
  putStrLn "}"
    where
      printTree n = do
        let facs = prime_factors n
        forM_ (nub facs) $ \f -> do
          putEdge n f
          let f' = product $ tail $ filter (==f) facs
          putEdge n f'

prime_factors n =
  case factors of
    [] -> [n]
    _  -> factors ++ prime_factors (n `div` (head factors))
  where factors = take 1 $ filter (\x -> (n `mod` x) == 0) [2 .. n-1]

putEdge a b = 
  putStrLn $ "    " ++ (show a) ++ " -> " ++ (show b)