RosettaCodeData/Task/Hamming-numbers/00DESCRIPTION

'''[[wp:Hamming numbers|Hamming numbers]]''' are numbers of the form  
       <big><big> H  =  2<sup>i</sup> &times; 3<sup>j</sup> &times; 5<sup>k</sup> </big></big>
where
       <big>      i, j, k  ≥  0 </big>

''Hamming numbers'' &nbsp; are also known as &nbsp; ''ugly numbers'' &nbsp; and also &nbsp; ''5-smooth numbers'' &nbsp; (numbers whose prime divisors are less or equal to 5).


;Task:
Generate the sequence of Hamming numbers, ''in increasing order''. &nbsp; In particular:
# Show the &nbsp; first twenty &nbsp; Hamming numbers.
# Show the &nbsp; 1691<sup>st</sup> &nbsp; Hamming number (the last one below &nbsp; 2<sup>31</sup>).
# Show the &nbsp; one million<sup>th</sup> &nbsp; Hamming number (if the language – or a convenient library – supports arbitrary-precision integers).


;Related tasks:
* [https://rosettacode.org/wiki/Humble_numbers humble numbers]


;References:
* Wikipedia entry: &nbsp; [[wp:Hamming numbers|Hamming numbers]] &nbsp; &nbsp; (this link is re-directed to &nbsp; '''Regular number''').
* Wikipedia entry: &nbsp; [[wp:Smooth number|Smooth number]]
* OEIS entry: &nbsp; [[oeis:A051037|A051037 &nbsp; 5-smooth &nbsp; or &nbsp; Hamming numbers]]
* [http://dobbscodetalk.com/index.php?option=com_content&task=view&id=913&Itemid=85 Hamming problem] from Dr. Dobb's CodeTalk (dead link as of Sep 2011; parts of the thread [http://drdobbs.com/blogs/architecture-and-design/228700538 here] and [http://www.jsoftware.com/jwiki/Essays/Hamming%20Number here]).
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