Count in factors

Count in factors is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Write a program which counts up from 1, displaying each number as the multiplication of its prime factors. For the purpose of this task, $1$ may be shown as itself.

For examle, $2$ is prime, so it would be shown as itself. $6$ is not prime; it would be shown as $2\times 3$. Likewise, 2144 is not prime; it would be shown as $2\times 2\times 2\times 2\times 2\times 67$.

Perl 6

The two multi prime lines are adapted from Perl 6's entry at Primality by Trial Division. <lang perl6>multi prime (Int $n --> Bool) {

   $n %% none 2, 3, *+2 ...^ * > sqrt $n;

}

multi prime (Int $n where ( $n <= 1)) {

   False;

}

sub next_prime(Int $start --> Int) {

   my $check = $start + 1;
   if ( $check %% 2 and $check > 2 ) { ++$check }

   until(prime($check)) { $check += 2 }

   return $check;

}

my @primes := 2, -> $a { next_prime($a) } ... *;

say "1: 1";

for(2..*) {

 print "$_: ";
 #say "L1 ... $_";
 my $toFactor = $_;
 my $currentProduct = 1;
 # It's not prime? Find its prime factors.
 until(1 == $toFactor)
 {
   # Iterate through our primes until we find a prime number that's a factor of $toFactor.
   my $prime_index = 0;
   
   until( $toFactor %% @primes[$prime_index]) { ++$prime_index };

   # We found our next factor.
   my $factor = @primes[$prime_index];

   if($currentProduct == 1) { print $factor } else { print " x $factor" }

   # Bookkeeping, to keep track of how far we have to go.
   $toFactor /= $factor;
   $currentProduct *= $factor;

 }
 say "";

}</lang>

The first twenty numbers:

1: 1
2: 2
3: 3
4: 2 x 2
5: 5
6: 2 x 3
7: 7
8: 2 x 2 x 2
9: 3 x 3
10: 2 x 5
11: 11
12: 2 x 2 x 3
13: 13
14: 2 x 7
15: 3 x 5
16: 2 x 2 x 2 x 2
17: 17
18: 2 x 3 x 3
19: 19
20: 2 x 2 x 5