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 A175441 Denominators of the harmonic means H(n) of the first n positive integers. 8
 1, 3, 11, 25, 137, 49, 363, 761, 7129, 7381, 83711, 86021, 1145993, 1171733, 1195757, 2436559, 42142223, 14274301, 275295799, 11167027, 18858053, 19093197, 444316699, 1347822955, 34052522467, 34395742267, 312536252003, 315404588903, 9227046511387, 9304682830147 (list; graph; refs; listen; history; text; internal format)
 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 a(n) coincides with A001008(n) iff n is not in the sequence A256102. For the quotient A001008(n) / a(n) if n is from A256102 see the corresponding entry of A256103. - Wolfdieter Lang, Apr 23 2015 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 FORMULA a(n) = numerator(sum(1/(k*(k+n)), k=1..oo)). - Paolo P. Lava, Jan 17 2013 a(n) = denominator(n/(Sum_{k=1..n} 1/k)). - Andrew Howroyd, Jan 08 2020 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 Cf. A102928 (numerators), A001008, A256102, A256103. Sequence in context: A190476 A060746 A111935 * A001008 A231606 A096617 Adjacent sequences: A175438 A175439 A175440 * A175442 A175443 A175444 KEYWORD nonn,easy,frac AUTHOR Jaroslav Krizek, May 16 2010 EXTENSIONS Terms a(25) and beyond from Andrew Howroyd, Jan 08 2020 STATUS approved

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Last modified September 26 20:30 EDT 2023. Contains 365668 sequences. (Running on oeis4.)