OFFSET
1,2
COMMENTS
See A102928 - numerators of the harmonic means of the first n positive integers.
a(n) = A001008(n) for n = 1 - 19 and other n.
a(n) is also the numerator of H(n)/(n+1)+1/(n+1)^2 = -int(x^n*log(1-x), x=0..1) with H(n) = A001008(x)/A002805(n) harmonic number of order n. - Groux Roland, Jan 08 2011
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
FORMULA
a(n) = denominator(n/(Sum_{k=1..n} 1/k)). - Andrew Howroyd, Jan 08 2020
a(n) = numerator(Sum_{k>0} 1/(k*(k+n))). - Mohammed Yaseen, Jun 23 2024
EXAMPLE
H(n) = 1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363, 2240/761, ...
Comparison with A001008: the first 19 entries coincide because 20 is the first entry of A256102; indeed, A001008(20) = 55835135 and a(2) = 11167027. The quotient is 5 = A256103(1). - Wolfdieter Lang, Apr 23 2015
MATHEMATICA
Table[Denominator[HarmonicMean[Range[n]]], {n, 30}] (* Harvey P. Dale, May 21 2021 *)
PROG
(PARI) a(n)={denominator(n/sum(k=1, n, 1/k))} \\ Andrew Howroyd, Jan 08 2020
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Jaroslav Krizek, May 16 2010
EXTENSIONS
Terms a(25) and beyond from Andrew Howroyd, Jan 08 2020
STATUS
approved