main :: [sys_message]
main = [Stdout (table 5 16 taskOutput),
        Stdout ("Found " ++ show (#taskOutput) ++ " Smith numbers.\n")]
       where taskOutput = takewhile (<= 10000) smiths

table :: num->num->[num]->[char]
table cw w ns = lay (map concat (split (map fmt ns)))
                where split [] = []
                      split ls = take w ls : split (drop w ls)
                      fmt n    = reverse (take cw ((reverse (shownum n)) ++ repeat ' '))

smiths :: [num]
smiths = filter smith [1..]

smith :: num->bool
smith n = (~ prime) & digsum n = sum (map digsum facs)
          where facs  = factors n
                prime = #facs <= 1

digsum :: num->num
digsum 0 = 0
digsum n = n mod 10 + digsum (n div 10)

factors :: num->[num]
factors = f [] 2
          where f acc d n = acc,                   if d>n
                          = f (d:acc) d (n div d), if n mod d = 0
                          = f acc (d+1) n,         otherwise