cp's OEIS Frontend

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

%I A186722 #24 Mar 29 2025 15:31:11
%S A186722 1,5,205,5369,1968329,240505109,822968714749,238820721143261,
%T A186722 354019312583809,10383930672892966877209,8745363341445960333910369,
%U A186722 33729537728506506466441425661,46252969210499754415427421586309,11115284554577186575391010113969347,20577813589884143264711540636313749803
%N A186722 a(n) = numerator of Sum_{k=1..p-1} 1/k^2 for p the n-th prime.
%D A186722 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 22-23.
%H A186722 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 A186722 f3:=proc(n) local p;
%p A186722 p:=ithprime(n);
%p A186722 numer(add(1/i^2,i=1..p-1));
%p A186722 end proc;
%p A186722 [seq(f3(n),n=1..20)];
%t A186722 Table[Numerator[HarmonicNumber[Prime[n]-1, 2]], {n, 1, 15}] (* _Jean-François Alcover_, Nov 29 2017 *)
%o A186722 (PARI) a(n) = my(p=prime(n)); numerator(sum(k=1, p-1, 1/k^2)); \\ _Michel Marcus_, Apr 05 2015
%Y A186722 Cf. A125551, A186720, A061002.
%K A186722 nonn
%O A186722 1,2
%A A186722 _N. J. A. Sloane_, Jan 21 2012