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

3,1

Comments

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

Links

Table of n, a(n) for n=3..13.

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

Maple

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)];

Mathematica

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 *)

Crossrefs

Cf. A061002, A034602, A186720, A186722.

Sequence in context: A246642 A167737 A268993 * A087856 A010957 A346981

Adjacent sequences: A125548 A125549 A125550 * A125552 A125553 A125554

Keyword

nonn

Author

Artur Jasinski, Jan 03 2007

Status

approved