A125551 - OEIS

%I #12 Nov 20 2019 18:16:53

%S 41,767,178939,18500393,48409924397,12569511639119,15392144025383,

%T 358066574927343685421,282108494885353559158399,

%U 911609127797473147741660153,1128121200256091571107985892349

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

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

%H 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, 2011

%p f1:=proc(n) local p;

%p p:=ithprime(n);

%p (1/p)*numer(add(1/i^2,i=1..p-1));

%p end proc;

%p [seq(f1(n),n=3..20)];

%t a = {}; Do[AppendTo[a, (1/(Prime[x]))Numerator[Sum[1/x^2, {x, 1, Prime[x] - 1}]]], {x, 3, 50}]; a

%t Table[Sum[1/k^2,{k,p-1}]/p,{p,Prime[Range[3,20]]}]//Numerator (* _Harvey P. Dale_, Nov 20 2019 *)

%Y Cf. A061002, A034602, A186720, A186722.

%K nonn

%O 3,1

%A _Artur Jasinski_, Jan 03 2007