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 A161893 #13 Aug 15 2022 08:55:10
%S A161893 4,3,18,22,30,9,11,50,15,17,78,44,48,27,122,33,72,39,170,92,198,210,
%T A161893 57,61,258,274,73,77,81,172,362,382,200,105,438,228,240,502,526,137,
%U A161893 566,590,153,638,658,171,714,734,189,786,818,842,217,890,914,237,974,1006,1038,532,1098,564,289,297
%N A161893 Denominators of S(n) = Sum_{j=2..n} (pi((j+1)^2) - pi(j^2))/(pi((j+1)^2)*pi(j^2)) where pi(k) = A000720(k).
%C A161893 The sum converges rapidly to 1/2; S(100) = 0.4992..., S(500) = 0.49995....
%e A161893 First few fractions are 1/4, 1/3, 7/18, 9/22, 13/30, 4/9, 5/11, 23/50, 7/15, ...
%o A161893 (PARI) a(n) = denominator(sum(k=2, n, (primepi((k+1)^2) - primepi(k^2))/(primepi((k+1)^2)*primepi(k^2)))); \\ _Michel Marcus_, Aug 15 2022
%Y A161893 Cf. A000720 (pi), A161892 (numerators).
%Y A161893 Cf. A161621.
%K A161893 nonn,frac,less
%O A161893 2,1
%A A161893 _Daniel Tisdale_, Jun 21 2009
%E A161893 Offset 2 and more terms from _Michel Marcus_, Aug 15 2022