The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A027611 Denominator of n * n-th harmonic number. 22
 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; text; internal format)
 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/(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_{d=2..n-1, n mod d > 0} n/d. Numerator = A079076. - Reinhard Zumkeller, Dec 21 2002 a(n) is odd iff n is a power of 2. - Benoit Cloitre, Oct 03 2002 Indices where a(n) differs from A128438 are terms of A074791. - Gary Detlefs, Sep 03 2011 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Complete Set FORMULA From Vladeta Jovovic, Sep 02 2002: (Start) a(n) = denominators of coefficients in expansion of -log(1-x)/(1-x)^2. a(n) = denominators of (n+1)*(harmonic(n+1) - 1). a(n) = denominators of (n+1)*(Psi(n+2) + Euler-gamma - 1). (End) 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. - Gary Detlefs, Sep 03 2011 a(n) = A213999(n, n-2) for n > 1. - Reinhard Zumkeller, Jul 03 2012 a(n) = denominators of coefficients of e.g.f. -1 + exp(x)*(1 + Sum_{j >= 0} (-x)^(j+1)/(j * j!)). - G. C. Greubel, Aug 24 2022 MAPLE a := n -> denom(add((n-j)/j, j=1..n)); seq(a(n), n = 1..30); # Peter Luschny, May 12 2023 MATHEMATICA a[n_]:=Denominator[n*HarmonicNumber[n]]; Array[a, 100] (* Vladimir Joseph Stephan Orlovsky, Feb 16 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 (Python) from sympy import harmonic def A027611(n): return (n*harmonic(n)).q # Chai Wah Wu, Sep 26 2021 (SageMath) [denominator(n*harmonic_number(n)) for n in (1..40)] # G. C. Greubel, Aug 24 2022 CROSSREFS Harmonic numbers = A001008/A002805. Cf. A001705, A006675, A027612, A049820, A024816. Cf. A128438, A074791, A079076. Sequence in context: A081526 A075711 A079077 * A303221 A345049 A168059 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 25 09:13 EDT 2024. Contains 371967 sequences. (Running on oeis4.)