Problem Statement

A   k-Almost-prime   is a natural number

n

{\displaystyle n}

that is the product of

k

{\displaystyle k}

(possibly identical) primes.

1-almost-primes,   where

k

1

{\displaystyle k=1}

,   are the prime numbers themselves. 2-almost-primes,   where

k

2

{\displaystyle k=2}

,   are the   semiprimes.

Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for

1 <= K <= 5

{\displaystyle 1<=K<=5}

.

Let's start with the solution:

: kprime?( n k -- b )
| i |
   0 2 n for: i [ 
      while( n i /mod swap 0 = ) [ ->n 1+ ] drop 
      ] 
   k == 
;
 
: table( k -- [] )
| l |
   Array new dup ->l
   2 while (l size 10 <>) [ dup k kprime? if dup l add then 1+ ]
   drop 
;