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A175441 Denominator of the harmonic mean H(n) of the first n positive integers. 10

%I #37 Feb 18 2024 08:28:11

%S 1,3,11,25,137,49,363,761,7129,7381,83711,86021,1145993,1171733,

%T 1195757,2436559,42142223,14274301,275295799,11167027,18858053,

%U 19093197,444316699,1347822955,34052522467,34395742267,312536252003,315404588903,9227046511387,9304682830147

%N Denominator of the harmonic mean H(n) of the first n positive integers.

%C See A102928 - numerators of the harmonic means of the first n positive integers.

%C a(n) = A001008(n) for n = 1 - 19 and other n.

%C 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

%C 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

%H Andrew Howroyd, <a href="/A175441/b175441.txt">Table of n, a(n) for n = 1..200</a>

%F a(n) = denominator(n/(Sum_{k=1..n} 1/k)). - _Andrew Howroyd_, Jan 08 2020

%e H(n) = 1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363, 2240/761, ...

%e 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

%t Table[Denominator[HarmonicMean[Range[n]]],{n,30}] (* _Harvey P. Dale_, May 21 2021 *)

%o (PARI) a(n)={denominator(n/sum(k=1, n, 1/k))} \\ _Andrew Howroyd_, Jan 08 2020

%Y Cf. A102928 (numerators), A001008, A256102, A256103.

%K nonn,easy,frac

%O 1,2

%A _Jaroslav Krizek_, May 16 2010

%E Terms a(25) and beyond from _Andrew Howroyd_, Jan 08 2020

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)