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


 
proc humble? x {
   foreach f {2 3 5 7} {
      while {$x % $f == 0} {set x [expr {$x / $f}]}
   }
   return [expr {$x == 1}]
}
set t1 {}
for {set i 1} {[llength $t1] < 50} {incr i} {
   if [humble? $i] {lappend t1 $i}
}
puts $t1
 