type PosInt = Int  -- lightweight type synonym for integers > 0

divides :: PosInt -> PosInt -> Bool
x `divides` y = (y `mod` x == 0)

divisors :: PosInt -> [PosInt]
divisors n = filter (`divides` n) [1 .. n `div` 2]

combinations :: [a] -> [[a]]
combinations [] = [[]]
combinations (x:xs) = concatMap (\c -> [c, x:c]) (combinations xs)

isPractical :: Int -> Bool
isPractical n | n < 1  =  error "isPractical: n must be positive"
isPractical n =
  let sums = map sum . combinations . divisors $ n in
  all (`elem` sums) [2 .. n-1]
      
main :: IO ()
main =
  putStrLn . show . sum . take 100 . filter isPractical $ [1..]