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%I #9 Sep 08 2022 08:46:24
%S 1,5,17,71,379,389,2843,5791,52679,54191,601141,608071,8071243,
%T 8148463,8196511,2060389,35567153,11912441,227867909,28847227,8275057,
%U 33289183,768422549,6163315597,30969555953,31263744353,94216171859,665249876813,19372559860777,19394741666137,603566081213047
%N Numerator 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[Numerator[Sum[1/(k*(Prime[k+1]-Prime[k])),{k,n}]],{n,40}] (* _Vincenzo Librandi_, Sep 27 2019 *)
%o (Magma) [Numerator(&+[1/(i*(NthPrime(i+1)-NthPrime(i))): i in [1..n]]): n in [1..35]]; // _Vincenzo Librandi_, Sep 27 2019
%Y Cf. A324801.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, Sep 11 2019
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