Humble numbers are positive integers which have &nbsp; no &nbsp; prime factors &nbsp; <big> &gt; </big> &nbsp; '''7'''.


Humble numbers are also called &nbsp; ''7-smooth numbers'', &nbsp; and sometimes called &nbsp; ''highly composite'', 
<br>although this conflicts with another meaning of &nbsp; ''highly composite numbers''.



Another way to express the above is:

  <big><big> humble  =  2<sup>i</sup> &times; 3<sup>j</sup> &times; 5<sup>k</sup> &times; 7<sup>m</sup> </big></big>

            where   <big>  i, j, k, m <big>&ge;</big> 0 </big>


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


;Related tasks:
:* &nbsp; [[Hamming numbers]]


;References:
:* &nbsp; [[wp:Smooth_number#Definition_smooth_numbers|Wikipedia: Smooth numbers]], see the 2<sup>nd</sup> paragraph.
:* &nbsp; [[oeis:A002473|OEIS A002473: humble numbers]]
:* &nbsp; [http://www.informatik.uni-ulm.de/acm/Locals/1996/number.sol University of Ulm, The first 5842 terms of humble numbers]
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