OFFSET
1,2
COMMENTS
See A175441 - denominators of the harmonic means of the first n positive integers. - Jaroslav Krizek, May 16 2010
a(n) is also the denominator of H(n-1)/n + 1/n^2 = -Integral_{x=0..1} x^n*log(1-x) with H(n) = A001008(n)/A002805(n) the harmonic number of order n. - Groux Roland, Jan 08 2011 [corrected by Gary Detlefs, Oct 06 2011]
Equivalently, a(n) is the reduced denominator of the arithmetic mean of the reciprocals of the first n positive integers (corresponding reduced numerator is A175441(n)). - Rick L. Shepherd, Jun 15 2014
n divides a(n) iff n is not from the sequence A256102. - Wolfdieter Lang, Apr 23 2015
LINKS
Stefano Spezia, Table of n, a(n) for n = 1..2000
Eric Weisstein's World of Mathematics, Harmonic Mean
FORMULA
a(n) = denominator(EulerGamma/n + PolyGamma(0, 1 + n)/n). - Artur Jasinski, Nov 02 2008
a(n) = numerator(n/H(n)), where H(n) is the n-th harmonic number. - Gary Detlefs, Sep 10 2011
a(n) = denominator((1/n)*Sum_{k=1..n} k + 1/k). - Stefano Spezia, Jul 27 2022
a(n) = denominator(Sum_{k>0} 1/(k*(k+n))). - Mohammed Yaseen, Jun 23 2024
EXAMPLE
1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363, 2240/761, ...
Division property: The first n not dividing a(n) is 20 because 20 = A256102(1). Indeed, a(20) = 62078016. - Wolfdieter Lang, Apr 23 2015
MATHEMATICA
Table[Numerator[n/HarmonicNumber[n]], {n, 26}]
PROG
(PARI) a(n) = numerator(n/sum(k=1, n, 1/k)); \\ Michel Marcus, Jul 29 2022
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Jan 19 2005
EXTENSIONS
Definition edited by N. J. A. Sloane, Jan 24 2024
STATUS
approved