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Search: id:A112287
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| A112287 |
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a(n) = denominator of sum of reciprocals of the terms of the continued fraction for H(n) = sum{k=1 to n} 1/k. |
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+0
7
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| 1, 2, 5, 12, 24, 4, 5, 35, 420, 156, 300, 45, 15, 39, 15351, 72, 1848, 10675, 300, 2142, 36, 5460, 15, 1870, 90, 63, 2040, 120, 138600, 3960, 1750320, 1324895, 440, 3945480, 5220, 158340, 1680, 3341100, 498960, 48048, 1260, 69264, 1510, 1168200, 568260
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Eric Weisstein's World of Mathematics, Harmonic Number
Eric Weisstein's World of Mathematics, Continued Fraction
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EXAMPLE
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1 +1/2 +1/3 +1/4 +1/5 +1/6 = 49/20 = 2 + 1/(2 + 1/(4 + 1/2)).
So a(6) is 4, the denominator of 7/4 = 1/2 + 1/2 + 1/4 + 1/2.
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MATHEMATICA
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f[n_] := Plus @@ (1/# &) /@ ContinuedFraction[Sum[1/k, {k, n}]]; Table[Denominator[f[n]], {n, 45}] (*Chandler*)
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CROSSREFS
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m-th harmonic number H(m) = A001008(m)/A002805(m).
Cf. A055573, A058027, A100398, A110020, A112286.
Sequence in context: A115520 A116735 A096376 this_sequence A127787 A116733 A116721
Adjacent sequences: A112284 A112285 A112286 this_sequence A112288 A112289 A112290
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KEYWORD
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nonn,frac
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Sep 01 2005
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EXTENSIONS
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Extended by Hans Havermann and Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 06 2005
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