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 A119686 #15 Feb 16 2025 08:33:01
%S A119686 1,5,21,193,4861,2443,78401,707209,85701889,4203312961,841345613,
%T A119686 841819933,4211020661,4212763061,2229320057669,376856710434461,
%U A119686 317005189060740101,317069381268836117,317122432680485717
%N A119686 Numerator of Sum_{k=1..n} 1/(prime(k) - 1)^2.
%C A119686 Lim_{n -> infinity} a(n)/A334746(n) = A086242.
%H A119686 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>.
%F A119686 a(n) = numerator(Sum_{k=1..n} 1/(Prime(k) - 1)^2).
%e A119686 The first few fractions are 1, 5/4, 21/16, 193/144, 4861/3600, 2443/1800, 78401/57600, 707209/518400, ... = A119686/A334746.
%t A119686 (* First program *)
%t A119686 Numerator[Table[Sum[1/(Prime[i]-1)^2,{i,1, n}], {n,1,30}]]
%t A119686 (* Second program *)
%t A119686 Numerator[Accumulate[1/(Prime[Range[20]]-1)^2]] (* _Harvey P. Dale_, Jun 28 2017 *)
%o A119686 (PARI) a(n)=numerator(sum(k=1,n,1/(prime(k)-1)^2)) \\ _Charles R Greathouse IV_, Apr 24 2015
%Y A119686 Cf. A000040, A006093, A086242, A334746 (denominators).
%K A119686 frac,nonn
%O A119686 1,2
%A A119686 _Alexander Adamchuk_, Jun 08 2006