53 lines
2.9 KiB
Text
53 lines
2.9 KiB
Text
'''n-smooth''' numbers are positive integers which have no prime factors <big> > </big> '''n'''.
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The '''n''' in the expression '''n-smooth''' is always prime;
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<br>there are <u>no</u> '''9-smooth''' numbers.
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'''1''' (unity) is always included in n-smooth numbers.
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<br>2-smooth numbers are non-negative powers of two.
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<br>5-smooth numbers are also called [[Hamming numbers]].
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<br>7-smooth numbers are also called [[humble numbers]].
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A way to express 11-smooth numbers is:
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<big><big> 11-smooth = 2<sup>i</sup> × 3<sup>j</sup> × 5<sup>k</sup> × 7<sup>m</sup> × 11<sup>p</sup></big></big>
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where <big> i, j, k, m, p ≥ 0 </big>
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;Task:
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:* calculate and show the first '''25''' n-smooth numbers for '''n=2''' ───► '''n=29'''
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:* calculate and show three numbers starting with '''3,000''' n-smooth numbers for '''n=3''' ───► '''n=29'''
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:* calculate and show twenty numbers starting with '''30,000''' n-smooth numbers for '''n=503''' ───► '''n=521''' (optional)
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All ranges (for '''n''') are to be inclusive, and only prime numbers are to be used.
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<br>The (optional) n-smooth numbers for the third range are: '''503''', '''509''', and '''521'''.
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<br>Show all n-smooth numbers for any particular '''n''' in a horizontal list.
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<br>Show all output here on this page.
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;Related tasks:
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:* [[Hamming numbers]]
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:* [[humble numbers]]
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;References:
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:* Wikipedia entry: [[wp:Hamming numbers|Hamming numbers]] (this link is re-directed to '''Regular number''').
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:* Wikipedia entry: [[wp:Smooth number|Smooth number]]
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:* OEIS entry: [[oeis:A000079|A000079 2-smooth numbers or non-negative powers of two]]
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:* OEIS entry: [[oeis:A003586|A003586 3-smooth numbers]]
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:* Mintz 1981: [https://www.fq.math.ca/Scanned/19-4/mintz.pdf 3-smooth numbers]
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:* OEIS entry: [[oeis:A051037|A051037 5-smooth numbers or Hamming numbers]]
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:* OEIS entry: [[oeis:A002473|A002473 7-smooth numbers or humble numbers]]
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:* OEIS entry: [[oeis:A051038|A051038 11-smooth numbers]]
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:* OEIS entry: [[oeis:A080197|A080197 13-smooth numbers]]
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:* OEIS entry: [[oeis:A080681|A080681 17-smooth numbers]]
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:* OEIS entry: [[oeis:A080682|A080682 19-smooth numbers]]
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:* OEIS entry: [[oeis:A080683|A080683 23-smooth numbers]]
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<br><br>
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