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 A375528 #17 Oct 20 2024 23:42:45
%S A375528 1,2,6,42,630,57330,219172590,2287458514758690,
%T A375528 523246645674205487113407810300,
%U A375528 34223381526163442974989472671319545640510650941743506071550,65068880171408068403202506207461768112305307530373013598603234255112994800902512713302330140957468591804616490482800
%N A375528 a(n) = denominator of Sum_{k = 1..n} 1 / (A000959(k)*A375527(k)).
%C A375528 The first few sums S(n) = Sum_{k = 1..n} 1/(A000959(k)*A375527(k)) are: 1/2, 5/6, 41/42, 629/630, 57329/57330,
%C A375528 219172589/219172590, 2287458514758689/2287458514758690,
%C A375528 523246645674205487113407810299/523246645674205487113407810300, ..., and the first 10 or 11 of these sums have the form (c-1)/c, where c is an integer. The present sequence gives the denominators.
%C A375528 For the harmonic series analog, A374663, _Rémy Sigrist_ has shown that all the partial sums have that form (see A374983), and for the prime number analog, A375581, it seems that all partial sums except for n = 4 and 6 have this property (see A375521/A375522).
%H A375528 N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]
%Y A375528 Cf. A000959, A375527, A374683, A374983/A375516, A375582, A375521/A375522.
%K A375528 nonn
%O A375528 1,2
%A A375528 _N. J. A. Sloane_, Sep 01 2024