Humble numbers are positive integers which have   no   prime factors    >    7.



Humble numbers are also called   7-smooth numbers,   and sometimes called   highly composite,

although this conflicts with another meaning of   highly composite numbers.



Another way to express the above is:

  humble  =  2i × 3j × 5k × 7m 

           where     i, j, k, m ≥ 0 



Task

   show the first   50   humble numbers   (in a horizontal list)
   show the number of humble numbers that have   x   decimal digits for all   x's   up to   n   (inclusive).
   show   (as many as feasible or reasonable for above)   on separate lines
   show all output here on this page


Related tasks

   Hamming numbers


References

   Wikipedia: Smooth numbers, see the 2nd paragraph.
   OEIS A002473: humble numbers
   University of Ulm, The first 5842 terms of humble numbers


  ' [ 2 3 5 7 ] smoothwith 
      [ -1 peek [ 10 12 ** ] constant = ]
  -1 split drop
  dup 50 split drop echo cr cr 
  12 times 
    [ dup 0 over size
      rot 10 i^ 1+ ** searchwith < 
      drop split swap size echo 
      sp i^ 1+ echo 
      say "-digit humble numbers" cr ] 
  drop 
 