A334746 Denominator of Sum_{k=1..n} 1/(prime(k) - 1)^2.

1, 4, 16, 144, 3600, 1800, 57600, 518400, 62726400, 3073593600, 614718720, 614718720, 3073593600, 3073593600, 1625931014400, 274782341433600, 231091949145657600, 231091949145657600, 231091949145657600, 231091949145657600, 77030649715219200

Offset

1,2

Comments

Lim_{n -> infinity} A119686(n)/a(n) = A086242.

Links

Table of n, a(n) for n=1..21.

Eric Weisstein's World of Mathematics, Prime Sums.

Example

The first few fractions are 1, 5/4, 21/16, 193/144, 4861/3600, 2443/1800, 78401/57600, 707209/518400, ... = A119686/A334746.

Mathematica

Denominator @ Accumulate @ Table[1/(Prime[k] - 1)^2, {k, 1, 21}] (* Amiram Eldar, May 12 2020 *)

Prog

(PARI) a(n) = denominator(sum(k=1, n, 1/(prime(k) - 1)^2)); \\ Michel Marcus, May 12 2020

Crossrefs

Cf. A000040, A006093, A086242, A119686 (numerators).

Sequence in context: A335400 A304193 A208661 * A262123 A005749 A005739

Adjacent sequences: A334743 A334744 A334745 * A334747 A334748 A334749

Keyword

nonn,frac

Author

Petros Hadjicostas, May 11 2020

Status

approved