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A186722 a(n) = numerator of Sum_{k=1..p-1} 1/k^2 for p the n-th prime. 1

%I #21 Nov 29 2017 12:26:55

%S 1,5,205,5369,1968329,240505109,822968714749,238820721143261,

%T 354019312583809,10383930672892966877209,8745363341445960333910369,

%U 33729537728506506466441425661,46252969210499754415427421586309,11115284554577186575391010113969347,20577813589884143264711540636313749803

%N a(n) = numerator of Sum_{k=1..p-1} 1/k^2 for p the n-th prime.

%H R. Mestrovic, <a href="http://arxiv.org/abs/1111.3057">Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011)</a>, arXiv:1111.3057 [math.NT], 2011.

%p f3:=proc(n) local p;

%p p:=ithprime(n);

%p numer(add(1/i^2,i=1..p-1));

%p end proc;

%p [seq(f3(n),n=1..20)];

%t Table[Numerator[HarmonicNumber[Prime[n]-1, 2]], {n, 1, 15}] (* _Jean-François Alcover_, Nov 29 2017 *)

%o (PARI) a(n) = my(p=prime(n)); numerator(sum(k=1, p-1, 1/k^2)); \\ _Michel Marcus_, Apr 05 2015

%Y Cf. A125551, A186720, A061002.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jan 21 2012

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)