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 A119686 Numerator of Sum_{k=1..n} 1/(prime(k) - 1)^2. 9
 1, 5, 21, 193, 4861, 2443, 78401, 707209, 85701889, 4203312961, 841345613, 841819933, 4211020661, 4212763061, 2229320057669, 376856710434461, 317005189060740101, 317069381268836117, 317122432680485717 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Lim_{n -> infinity} a(n)/A334746(n) = A086242. LINKS Eric Weisstein's World of Mathematics, Prime Sums. FORMULA a(n) = numerator(Sum_{k=1..n} 1/(Prime(k) - 1)^2). EXAMPLE The first few fractions are 1, 5/4, 21/16, 193/144, 4861/3600, 2443/1800, 78401/57600, 707209/518400, ... = A119686/A334746. MATHEMATICA (* First program *) Numerator[Table[Sum[1/(Prime[i]-1)^2, {i, 1, n}], {n, 1, 30}]] (* Second program *) Numerator[Accumulate[1/(Prime[Range[20]]-1)^2]] (* Harvey P. Dale, Jun 28 2017 *) PROG (PARI) a(n)=numerator(sum(k=1, n, 1/(prime(k)-1)^2)) \\ Charles R Greathouse IV, Apr 24 2015 CROSSREFS Cf. A000040, A006093, A086242, A334746 (denominators). Sequence in context: A140196 A027160 A195963 * A241467 A267020 A141798 Adjacent sequences:  A119683 A119684 A119685 * A119687 A119688 A119689 KEYWORD frac,nonn AUTHOR Alexander Adamchuk, Jun 08 2006 STATUS approved

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Last modified May 18 23:58 EDT 2021. Contains 344009 sequences. (Running on oeis4.)