Task

Write a program which counts up from   1,   displaying each number as the multiplication of its prime factors.

For the purpose of this task,   1   (unity)   may be shown as itself.



Example

      2   is prime,   so it would be shown as itself.

      6   is not prime;   it would be shown as   



2
×
3


{\displaystyle 2\times 3}

.
2144   is not prime;   it would be shown as   



2
×
2
×
2
×
2
×
2
×
67


{\displaystyle 2\times 2\times 2\times 2\times 2\times 67}

.



Related tasks

   prime decomposition
   factors of an integer
   Sieve of Eratosthenes
   primality by trial division
   factors of a Mersenne number
   trial factoring of a Mersenne number
   partition an integer X into N primes


(de factor (N)
   (make
      (let (D 2  L (1 2 2 . (4 2 4 2 4 6 2 6 .))  M (sqrt N))
         (while (>= M D)
            (if (=0 (% N D))
               (setq M (sqrt (setq N (/ N (link D)))))
               (inc 'D (pop 'L)) ) )
         (link N) ) ) )
 
(for N 20
   (prinl N ": " (glue " * " (factor N))) )