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


factorize(n){
	if n = 1
		return 1
	if n < 1
		return false
	result := 0, m := n, k := 2
	While n >= k{
		while !Mod(m, k){
			result .= " * " . k, m /= k
		}
		k++
	}
	return SubStr(result, 5)
}
Loop 22
   out .= A_Index ": " factorize(A_index) "`n"
MsgBox % out