DouKaku?

list max b n
    | (b^n) > max   =   []
    | otherwise = n : list max b (n+1)

scan n = [(n,i,j,k)|i<-list n 2 0,j<-list n 3 0,k<-list n 5 0,n == (2^i*3^j*5^k)]

result = take 100 $ concatMap (scan) $ filter (check) [1..]

check n
    | n == 1            =   True
    | (n `mod` 2) == 0  =   True
    | (n `mod` 3) == 0  =   True
    | (n `mod` 5) == 0  =   True
    | otherwise         =   False

main=do
    mapM (\x-> putStrLn $ format x) result
    where
        format (n,i,j,k) = concat [show n," = ",fmt 2 i," * ",fmt 3 j," * ",fmt 5 k]
        fmt b n = show b ++ "^" ++ show n