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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
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.
Sequence in context: A081526 A075711 A079077 * A303221 A345049 A168059
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

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