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

1, 5, 205, 5369, 1968329, 240505109, 822968714749, 238820721143261, 354019312583809, 10383930672892966877209, 8745363341445960333910369, 33729537728506506466441425661, 46252969210499754415427421586309, 11115284554577186575391010113969347, 20577813589884143264711540636313749803

Offset: 1

Author

N. J. A. Sloane, Jan 21 2012

Keywords

• nonn

References

• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 22-23.

Links

• R. Mestrovic, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057 [math.NT], 2011.

Crossrefs

Cf. A125551, A186720, A061002.

Programs

Maple

f3:=proc(n) local p;
p:=ithprime(n);
numer(add(1/i^2,i=1..p-1));
end proc;
[seq(f3(n),n=1..20)];

Mathematica

Table[Numerator[HarmonicNumber[Prime[n]-1, 2]], {n, 1, 15}] (* Jean-François Alcover, Nov 29 2017 *)

PARI

a(n) = my(p=prime(n)); numerator(sum(k=1, p-1, 1/k^2)); \\ Michel Marcus, Apr 05 2015