cp's OEIS Frontend

A175441 Denominator of the harmonic mean of the first n positive integers.

%I A175441 #43 Jun 23 2024 10:35:35
%S A175441 1,3,11,25,137,49,363,761,7129,7381,83711,86021,1145993,1171733,
%T A175441 1195757,2436559,42142223,14274301,275295799,11167027,18858053,
%U A175441 19093197,444316699,1347822955,34052522467,34395742267,312536252003,315404588903,9227046511387,9304682830147
%N A175441 Denominator of the harmonic mean of the first n positive integers.
%C A175441 See A102928 - numerators of the harmonic means of the first n positive integers.
%C A175441 a(n) = A001008(n) for n = 1 - 19 and other n.
%C A175441 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 A175441 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 A175441 Andrew Howroyd, <a href="/A175441/b175441.txt">Table of n, a(n) for n = 1..200</a>
%F A175441 a(n) = denominator(n/(Sum_{k=1..n} 1/k)). - _Andrew Howroyd_, Jan 08 2020
%F A175441 a(n) = numerator(Sum_{k>0} 1/(k*(k+n))). - _Mohammed Yaseen_, Jun 23 2024
%e A175441 H(n) = 1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363, 2240/761, ...
%e A175441 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 A175441 Table[Denominator[HarmonicMean[Range[n]]],{n,30}] (* _Harvey P. Dale_, May 21 2021 *)
%o A175441 (PARI) a(n)={denominator(n/sum(k=1, n, 1/k))} \\ _Andrew Howroyd_, Jan 08 2020
%Y A175441 Cf. A102928 (numerators), A001008, A256102, A256103.
%K A175441 nonn,easy,frac
%O A175441 1,2
%A A175441 _Jaroslav Krizek_, May 16 2010
%E A175441 Terms a(25) and beyond from _Andrew Howroyd_, Jan 08 2020