A125551 -id:A125551 - cp's OEIS frontend

A186720 As p runs through the primes, sequence gives denominator of Sum_{k=1..p-1} 1/k^2.

1, 4, 144, 3600, 1270080, 153679680, 519437318400, 150117385017600, 221193371393280, 6450247552370862240000, 5424658191543895143840000, 20852386088294732932920960000, 28546916554875489385168794240000, 6855338104106528236638391873920000, 12675520154492970709544386574878080000

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, A061002.

f2:=proc(n) local p;
p:=ithprime(n);
denom(add(1/i^2,i=1..p-1));
end proc;
[seq(f2(n),n=1..20)];

a[n_] := HarmonicNumber[Prime[n] - 1, 2] // Denominator;
Array[a, 15] (* Jean-François Alcover, Nov 25 2017 *)

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

A186720 As p runs through the primes, sequence gives denominator of Sum_{k=1..p-1} 1/k^2.

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