A119686 Numerator of Sum_{k=1..n} 1/(prime(k) - 1)^2.

1, 5, 21, 193, 4861, 2443, 78401, 707209, 85701889, 4203312961, 841345613, 841819933, 4211020661, 4212763061, 2229320057669, 376856710434461, 317005189060740101, 317069381268836117, 317122432680485717

Offset

1,2

Comments

Lim_{n -> infinity} a(n)/A334746(n) = A086242.

Links

Table of n, a(n) for n=1..19.

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