n-smooth   numbers are positive integers which have no prime factors  >  n.

The   n   (when using it in the expression)   n-smooth   is always prime,

there are   no   9-smooth numbers.

1   (unity)   is always included in n-smooth numbers.




2-smooth   numbers are non-negative powers of two.

5-smooth   numbers are also called   Hamming numbers.

7-smooth   numbers are also called    humble   numbers.



A way to express   11-smooth   numbers is:

  11-smooth  =  2i × 3j × 5k × 7m × 11p

           where     i, j, k, m, p ≥ 0  



Task

   calculate and show the first   25   n-smooth numbers   for   n=2   ───►   n=29
   calculate and show   three numbers starting with   3,000   n-smooth numbers   for   n=3   ───►   n=29
   calculate and show twenty numbers starting with  30,000   n-smooth numbers   for   n=503   ───►   n=521   (optional)


All ranges   (for   n)   are to be inclusive, and only prime numbers are to be used.

The (optional) n-smooth numbers for the third range are:   503,   509,   and   521.

Show all n-smooth numbers for any particular   n   in a horizontal list.

Show all output here on this page.



Related tasks

   Hamming numbers
   humble numbers


References

   Wikipedia entry:   Hamming numbers     (this link is re-directed to   Regular number).
   Wikipedia entry:   Smooth number
   OEIS entry:   A000079    2-smooth numbers or non-negative powers of two
   OEIS entry:   A003586    3-smooth numbers
   OEIS entry:   A051037    5-smooth numbers or Hamming numbers
   OEIS entry:   A002473    7-smooth numbers or humble numbers
   OEIS entry:   A051038   11-smooth numbers
   OEIS entry:   A080197   13-smooth numbers
   OEIS entry:   A080681   17-smooth numbers
   OEIS entry:   A080682   19-smooth numbers
   OEIS entry:   A080683   23-smooth numbers


 
  [ behead 0 swap rot
    witheach 
      [ 2dup < iff
          drop done
        nip nip 
        i^ 1+ swap ] ]               is smallest   ( [ --> n n )
 
  [ stack ]                          is end.test   (   --> s   )
 
  [ ]'[ end.test put
    dup temp put
    ' [ 1 ]
    0 rot size of
    [ over end.test share do if done
      [] unrot 
      dup dip
        [ witheach
            [ dip dup peek 
              temp share i^ peek *
              rot swap join swap ] ]
      rot smallest
      dip 
        [ 2dup peek 1+ unrot poke ]
      rot swap over
      -1 peek over = iff
        drop else join
      swap again ]
    drop
    end.test release
    temp release ]                   is smoothwith ( [ --> [   )
 
  [ ' [ 2 3 5 7 11 13 17 19 23 29 ] 
    swap split drop ]                is primes     ( n --> [   )
 
  10 times 
    [ i^ 1+ primes 
      smoothwith [ size 25 = ]
      echo cr ]
  cr
  9 times
    [ i^ 2 + primes
      smoothwith [ size 3002 = ]
      -3 split nip echo cr ]