This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A102928 #78 Feb 16 2025 08:32:56
%S A102928 1,4,18,48,300,120,980,2240,22680,25200,304920,332640,4684680,5045040,
%T A102928 5405400,11531520,208288080,73513440,1474352880,62078016,108636528,
%U A102928 113809696,2736605872,8566766208,223092870000,232016584800
%N A102928 Numerator of the harmonic mean of the first n positive integers.
%C A102928 See A175441 - denominators of the harmonic means of the first n positive integers. - _Jaroslav Krizek_, May 16 2010
%C A102928 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]
%C A102928 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
%C A102928 n divides a(n) iff n is not from the sequence A256102. - _Wolfdieter Lang_, Apr 23 2015
%H A102928 Stefano Spezia, <a href="/A102928/b102928.txt">Table of n, a(n) for n = 1..2000</a>
%H A102928 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicMean.html">Harmonic Mean</a>
%F A102928 a(n) = denominator(EulerGamma/n + PolyGamma(0, 1 + n)/n). - _Artur Jasinski_, Nov 02 2008
%F A102928 a(n) = numerator(n/H(n)), where H(n) is the n-th harmonic number. - _Gary Detlefs_, Sep 10 2011
%F A102928 a(n) = denominator((1/n)*Sum_{k=1..n} k + 1/k). - _Stefano Spezia_, Jul 27 2022
%F A102928 a(n) = denominator(Sum_{k>0} 1/(k*(k+n))). - _Mohammed Yaseen_, Jun 23 2024
%e A102928 1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363, 2240/761, ...
%e A102928 Division property: The first n not dividing a(n) is 20 because 20 = A256102(1). Indeed, a(20) = 62078016. - _Wolfdieter Lang_, Apr 23 2015
%t A102928 Table[Numerator[n/HarmonicNumber[n]], {n, 26}]
%o A102928 (PARI) a(n) = numerator(n/sum(k=1, n, 1/k)); \\ _Michel Marcus_, Jul 29 2022
%Y A102928 Cf. A001008, A175441, A256102.
%K A102928 nonn,frac
%O A102928 1,2
%A A102928 _Eric W. Weisstein_, Jan 19 2005
%E A102928 Definition edited by _N. J. A. Sloane_, Jan 24 2024