|
%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
|
