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
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
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