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%I #10 Sep 08 2022 08:46:24
%S 1,4,12,48,240,240,1680,3360,30240,30240,332640,332640,4324320,
%T 4324320,4324320,1081080,18378360,6126120,116396280,14549535,4157010,
%U 16628040,382444920,3059559360,15297796800,15297796800,45893390400,321253732800,9316358251200,9316358251200,288807105787200,144403552893600
%N Denominator of Sum_{k=1..n} 1/(k*(prime(k+1)-prime(k))).
%C The series Sum_{k=1..oo} 1/(k*(prime(k+1)-prime(k))) diverges.
%D D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.21, 1(b), p. 248.
%e 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, ...
%t Table[Denominator[Sum[1/(k*(Prime[k+1]-Prime[k])),{k,n}]],{n,40}] (* _Vincenzo Librandi_, Sep 27 2019 *)
%o (Magma) [Denominator(&+[1/(i*(NthPrime(i+1)-NthPrime(i))): i in [1..n]]): n in [1..35]]; // _Vincenzo Librandi_, Sep 27 2019
%Y Cf. A324800.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, Sep 11 2019
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