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Search: id:A110545
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| A110545 |
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a(n) is smallest positive integer m such that n divides either the numerator or the denominator of the (reduced) fraction H(m) = sum{k=1 to m} 1/k. |
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+0
3
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| 1, 2, 2, 4, 4, 3, 6, 8, 9, 5, 3, 4, 12, 7, 5, 16, 16, 9, 18, 5, 9, 11, 22, 9, 4, 13, 27, 7, 13, 5, 30, 32, 7, 17, 7, 9, 17, 19, 13, 8, 40, 9, 13, 11, 9, 23, 46, 16, 6, 25, 17, 13, 22, 27, 11, 8, 19, 29, 58, 5, 10, 31, 9, 64, 13, 11, 66, 17, 22, 7, 70, 9, 72, 37, 25, 19, 11, 13, 78, 16, 81
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For when a(n)=n, see A112875; this begins: 1,2,4,8,9,16,27,32,64,81,...,.
Conjecture: a(n)<=n for all positive n's.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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a(5) = 4 because H(4) = 25/12 is the first harmonic number with either its numerator or denominator divisible by 5.
a(6) = 3 because H(3) = 11/6 is the first harmonic number with either its numerator or denominator divisible by 6.
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MATHEMATICA
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f[n_] := Block[{h = k = 1}, While[ !IntegerQ[ Numerator[h]/n] && !IntegerQ[ Denominator[h]/n], k++; h = h + 1/k]; k]; Table[ f[n], {n, 81}] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A001008, A002805, A112875.
Sequence in context: A038674 A090277 A024222 this_sequence A104798 A143358 A143729
Adjacent sequences: A110542 A110543 A110544 this_sequence A110546 A110547 A110548
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Sep 11 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Sep 28 2005
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