A324801 Denominator of Sum_{k=1..n} 1/(k*(prime(k+1)-prime(k))).

1, 4, 12, 48, 240, 240, 1680, 3360, 30240, 30240, 332640, 332640, 4324320, 4324320, 4324320, 1081080, 18378360, 6126120, 116396280, 14549535, 4157010, 16628040, 382444920, 3059559360, 15297796800, 15297796800, 45893390400, 321253732800, 9316358251200, 9316358251200, 288807105787200, 144403552893600

Offset

1,2

Comments

The series Sum_{k=1..oo} 1/(k*(prime(k+1)-prime(k))) diverges.

References

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.21, 1(b), p. 248.

Links

Table of n, a(n) for n=1..32.

Example

1, 5/4, 17/12, 71/48, 379/240, 389/240, 2843/1680, 5791/3360, 52679/30240, 54191/30240, 601141/332640, 608071/332640, 8071243/4324320, ...

Mathematica

Table[Denominator[Sum[1/(k*(Prime[k+1]-Prime[k])), {k, n}]], {n, 40}] (* Vincenzo Librandi, Sep 27 2019 *)

Prog

(Magma) [Denominator(&+[1/(i*(NthPrime(i+1)-NthPrime(i))): i in [1..n]]): n in [1..35]]; // Vincenzo Librandi, Sep 27 2019

Crossrefs

Cf. A324800.

Sequence in context: A151483 A355800 A192622 * A111930 A335595 A197867

Adjacent sequences: A324798 A324799 A324800 * A324802 A324803 A324804

Keyword

nonn,frac

Author

N. J. A. Sloane, Sep 11 2019

Status

approved