32 lines
1.3 KiB
Text
32 lines
1.3 KiB
Text
Humble numbers are positive integers which have no prime factors <big> > </big> '''7'''.
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Humble numbers are also called ''7-smooth numbers'', and sometimes called ''highly composite'',
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<br>although this conflicts with another meaning of ''highly composite numbers''.
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Another way to express the above is:
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<big><big> humble = 2<sup>i</sup> × 3<sup>j</sup> × 5<sup>k</sup> × 7<sup>m</sup> </big></big>
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where <big> i, j, k, m <big>≥</big> 0 </big>
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;Task:
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:* show the first '''50''' humble numbers (in a horizontal list)
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:* show the number of humble numbers that have '''x''' decimal digits for all '''x's''' up to '''n''' (inclusive).
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:* show (as many as feasible or reasonable for above) on separate lines
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:* show all output here on this page
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;Related tasks:
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:* [[Hamming numbers]]
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;References:
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:* [[wp:Smooth_number#Definition_smooth_numbers|Wikipedia: Smooth numbers]], see the 2<sup>nd</sup> paragraph.
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:* [[oeis:A002473|OEIS A002473: humble numbers]]
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:* [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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<br><br>
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