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


HumbleGenerator[max_] := 
 Sort[Flatten@ParallelTable[
    2^i 3^j 5^k 7^m, {i, 0, Log[2, max]}, {j, 0, Log[3, max/2^i]}, {k,
      0, Log[5, max/(2^i 3^j)]}, {m, 0, Log[7, max/(2^i 3^j 5^k)]}]]
 
{"First 50 Humble Numbers:",
  HumbleGenerator[120],
  "\nDigits\[Rule]Count",
  Rule @@@ Tally[IntegerLength /@ Drop[HumbleGenerator[10^100], -1]] //
    Column} // Column