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%I #14 May 11 2020 20:00:15
%S 1,5,21,193,4861,2443,78401,707209,85701889,4203312961,841345613,
%T 841819933,4211020661,4212763061,2229320057669,376856710434461,
%U 317005189060740101,317069381268836117,317122432680485717
%N Numerator of Sum_{k=1..n} 1/(prime(k) - 1)^2.
%C Lim_{n -> infinity} a(n)/A334746(n) = A086242.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>.
%F a(n) = numerator(Sum_{k=1..n} 1/(Prime(k) - 1)^2).
%e The first few fractions are 1, 5/4, 21/16, 193/144, 4861/3600, 2443/1800, 78401/57600, 707209/518400, ... = A119686/A334746.
%t (* First program *)
%t Numerator[Table[Sum[1/(Prime[i]-1)^2,{i,1, n}], {n,1,30}]]
%t (* Second program *)
%t Numerator[Accumulate[1/(Prime[Range[20]]-1)^2]] (* _Harvey P. Dale_, Jun 28 2017 *)
%o (PARI) a(n)=numerator(sum(k=1,n,1/(prime(k)-1)^2)) \\ _Charles R Greathouse IV_, Apr 24 2015
%Y Cf. A000040, A006093, A086242, A334746 (denominators).
%K frac,nonn
%O 1,2
%A _Alexander Adamchuk_, Jun 08 2006
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