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


# To take advantage of gojq's arbitrary-precision integer arithmetic:
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
 
# Input: a non-negative integer determining when to stop
def count_in_factors:
  "1: 1",
  (range(2;.) | "\(.): \([factors] | join("x"))");
 
def count_in_factors($m;$n):
  if  . == 1 then  "1: 1" else empty end,
  (range($m;$n) | "\(.): \([factors] | join("x"))");
 