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
Keywords
Links
- R. Mestrovic, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057, 2011
Programs
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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)];
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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 *)
Comments