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 A055980 #24 Feb 16 2025 08:32:43
%S A055980 1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,
%T A055980 4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
%U A055980 4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5
%N A055980 a(n) = floor(Sum_{i=1..n} 1/i).
%C A055980 If we choose at random (uniformly) a permutation in the symmetric group S_n then a(n) is the expected number of cycles (rounded down) in the cycle decomposition of the permutation. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Oct 17 2001
%C A055980 a(n) = A214075(n,n-1) for n > 0. - _Reinhard Zumkeller_, Jul 03 2012
%H A055980 Reinhard Zumkeller, <a href="/A055980/b055980.txt">Table of n, a(n) for n = 1..10000</a>
%H A055980 L. D. Kudryavtsev, <a href="https://encyclopediaofmath.org/wiki/Harmonic_series">Harmonic series</a>, The Encyclopedia of Mathematics.
%H A055980 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/High-WaterMark.html">High-Water Mark</a>
%F A055980 a(n) ~ log(n) - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 25 2001
%F A055980 a(n) = floor[A001008(n)/A002805(n)]. - _Lekraj Beedassy_, Sep 17 2006
%t A055980 Floor[HarmonicNumber[Range[110]]] (* _Harvey P. Dale_, May 22 2021 *)
%o A055980 (Haskell)
%o A055980 import Data.Ratio ((%), denominator)
%o A055980 a055980 = floor . sum . map (1 %) . enumFromTo 1
%o A055980 a055980_list = map floor $ scanl1 (+) $ map (1 %) [1..]
%o A055980 -- _Reinhard Zumkeller_, Jul 03 2012
%Y A055980 Cf. A002387, A004080 (indices of records).
%K A055980 nonn
%O A055980 1,4
%A A055980 _Henry Bottomley_, Jul 20 2000