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A027611
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Denominator of n * n-th harmonic number.
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14
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1, 1, 2, 3, 12, 10, 20, 35, 280, 252, 2520, 2310, 27720, 25740, 24024, 45045, 720720, 680680, 4084080, 3879876, 739024, 235144, 5173168, 14872858, 356948592, 343219800, 2974571600, 2868336900, 80313433200, 77636318760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This is very similar to A128438, which is a different sequence. They differ at n=6 (and nowhere else?). - N. J. A. Sloane, Nov 21 2008
Denominator of 1/n + 2/(n-1) + 3/(n-2) + ... + (n-1)/2 + n.
Denominator of sum(k=1,n,frac(n/k)) where frac(x/y) denotes the fractional part of x/y. - Benoit Cloitre, Oct 03 2002
Denominator of Sum{n/d : 1<d<n and n mod d > 0}. Numerator = A079076. - Reinhard Zumkeller, Dec 21 2002
a(n) is odd iff n is a power of 2. - Benoit Cloitre, Oct 03 2002
a(n) equals the denominator of the (closed form) evaluation of Sum[HarmonicNumber[k+n-1],{k,1,r}] (see Mathematica code below). [From John M. Campbell, May 28, 2011]
Indices where a(n) differs from A128438 are terms of A074791. [From Gary Detlefs, Sep 03 2011]
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LINKS
| Eric Weisstein's World of Mathematics, Complete Set
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FORMULA
| Denominators of coefficients in expansion of -log(1-x)/(1-x)^2. Denominators of (n+1)*(harmonic(n+1)-1). Denominators of (n+1)*(Psi(n+2)+gamma-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 02 2002
a(n) = Numerator(h(n)/h(n-1))-Denominator(h(n)/h(n-1)), n>1, where h(n) is the n-th harmonic number. [From Gary Detlefs, Sep 03 2011]
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MATHEMATICA
| f[n_]:=Denominator[n*HarmonicNumber[n]]; Array[f, 100] (* From Vladimir Joseph Stephan Orlovsky, Feb 16 2011 *)
Table[Denominator[Sum[HarmonicNumber[k+n-1], {k, 1, r}]], {n, 2, 40}] (* From John M. Campbell, May 28, 2011 *)
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CROSSREFS
| Harmonic numbers = A001008/A002805. Cf. A001705, A006675, A027612, A049820, A024816.
Cf. A128438.
Sequence in context: A081526 A075711 A079077 * A168059 A068550 A093432
Adjacent sequences: A027608 A027609 A027610 * A027612 A027613 A027614
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KEYWORD
| nonn,easy,frac
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AUTHOR
| Glen Burch (gburch(AT)erols.com)
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EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com) following a suggestion of Eric Weisstein, Jul 02 2004.
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