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 A161527 #66 Jul 12 2025 08:35:13
%S A161527 1,2,11,27,61,809,13945,268027,565447,2358365,73551683,2734683311,
%T A161527 112599773191,4860900544813,9968041656757,40762420985117,
%U A161527 83151858555707,5085105491885327,341472595155548909,24295409051193284539,1777124696397561611347
%N A161527 Numerators of cumulative sums of rational sequence A038110(k)/A038111(k).
%C A161527 By rewriting the sequence of sums as 1 - Product_{n>=1} (1 - 1/prime(n)), one can show that the product goes to zero and the sequence of sums converges to 1. This is interesting because the terms approach 1/(2*prime(n)) for large n, and a sum of such terms might be expected to diverge, since Sum_{n>=1} 1/(2*prime(n)) diverges.
%C A161527 Denominators appear to be given by A060753(n+1). - _Peter Kagey_, Jun 08 2019
%C A161527 A254196 appears to be a duplicate of this sequence. - _Michel Marcus_, Aug 05 2019
%H A161527 Peter Kagey, <a href="/A161527/b161527.txt">Table of n, a(n) for n = 1..400</a>
%F A161527 a(n) = A053144(n)/A058250(n). - _Jamie Morken_, Aug 28 2022
%t A161527 Numerator[Table[1 - Product[1 - (1/Prime[k]), {k,1,n}], {n,1,20}]]
%o A161527 (PARI) r(n) = prod(k=1, n-1, (1 - 1/prime(k)))/prime(n);
%o A161527 a(n) = numerator(sum(k=1, n, r(k))); \\ _Michel Marcus_, Jun 08 2019
%Y A161527 Cf. A038110, A038111, A060753, A254196.
%K A161527 nonn,frac
%O A161527 1,2
%A A161527 _Daniel Tisdale_, Jun 12 2009