

A027611


Denominator of n * nth harmonic number.


18



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
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OFFSET

1,3


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/(n1) + 3/(n2) + ... + (n1)/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+n1],{k,1,r}] (see Mathematica code below).  John M. Campbell, May 28 2011
Indices where a(n) differs from A128438 are terms of A074791.  Gary Detlefs, Sep 03 2011
a(n) = A213999(n,n2) for n > 1.  Reinhard Zumkeller, Jul 03 2012


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Complete Set


FORMULA

Denominators of coefficients in expansion of log(1x)/(1x)^2. Denominators of (n+1)*(harmonic(n+1)1). Denominators of (n+1)*(Psi(n+2)+gamma1).  Vladeta Jovovic, Sep 02 2002
a(n) = Numerator(h(n)/h(n1))Denominator(h(n)/h(n1)), n>1, where h(n) is the nth harmonic number.  Gary Detlefs, Sep 03 2011


MATHEMATICA

f[n_]:=Denominator[n*HarmonicNumber[n]]; Array[f, 100] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2011 *)
Table[Denominator[Sum[HarmonicNumber[k+n1], {k, 1, r}]], {n, 2, 40}] (* John M. Campbell, May 28 2011 *)


PROG

(Haskell)
import Data.Ratio ((%), denominator)
a027611 n = denominator $ sum $ map (n %) [1..n]
 Reinhard Zumkeller, Jul 03 2012
(MAGMA) [Denominator(n*HarmonicNumber(n)): n in [1..40]]; // Vincenzo Librandi, Feb 19 2014
(PARI) a(n) = denominator(n*sum(k=1, n, 1/k)); \\ Michel Marcus, Feb 15 2015


CROSSREFS

Harmonic numbers = A001008/A002805.
Cf. A001705, A006675, A027612, A049820, A024816.
Cf. A128438.
Sequence in context: A081526 A075711 A079077 * A303221 A168059 A068550
Adjacent sequences: A027608 A027609 A027610 * A027612 A027613 A027614


KEYWORD

nonn,easy,frac


AUTHOR

Glen Burch (gburch(AT)erols.com)


EXTENSIONS

Entry revised by N. J. A. Sloane following a suggestion of Eric W. Weisstein, Jul 02 2004


STATUS

approved



