A186720 -id:A186720 - cp's OEIS frontend

A125551 As p runs through primes >= 5, sequence gives { numerator of Sum_{k=1..p-1} 1/k^2 } / p.

41, 767, 178939, 18500393, 48409924397, 12569511639119, 15392144025383, 358066574927343685421, 282108494885353559158399, 911609127797473147741660153, 1128121200256091571107985892349

Offset: 3

Artur Jasinski, Jan 03 2007

nonn

This is an integer by a theorem of Waring and Wolstenholme.

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

Cf. A061002, A034602, A186720, A186722.

f1:=proc(n) local p;
p:=ithprime(n);
(1/p)*numer(add(1/i^2,i=1..p-1));
end proc;
[seq(f1(n),n=3..20)];

a = {}; Do[AppendTo[a, (1/(Prime[x]))Numerator[Sum[1/x^2, {x, 1, Prime[x] - 1}]]], {x, 3, 50}]; a
Table[Sum[1/k^2,{k,p-1}]/p,{p,Prime[Range[3,20]]}]//Numerator (* Harvey P. Dale, Nov 20 2019 *)

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

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Jan 21 2012

nonn

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

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

Cf. A125551, A186720, A061002.

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)];

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

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

cp's OEIS Frontend

A125551 As p runs through primes >= 5, sequence gives { numerator of Sum_{k=1..p-1} 1/k^2 } / p.

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