|
|
A125551
|
|
As p runs through primes >= 5, sequence gives { numerator of Sum_{k=1..p-1} 1/k^2 } / p.
|
|
2
|
|
|
41, 767, 178939, 18500393, 48409924397, 12569511639119, 15392144025383, 358066574927343685421, 282108494885353559158399, 911609127797473147741660153, 1128121200256091571107985892349
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,1
|
|
COMMENTS
|
This is an integer by a theorem of Waring and Wolstenholme.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|