A127043 Primes p such that denominator of Sum_{k=1..p-1} 1/k^2 is not a square.

11, 13, 23, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 101, 103, 107, 109, 113, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421

Offset: 1

Author

Artur Jasinski, Jan 03 2007

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061002, A034602, A127029, A127042.

Programs

Maple

S:= 0: R:= NULL: count:= 0:
for k from 1 while count < 100 do
  S:= S + 1/k^2;
  if isprime(k+1) and not issqr(denom(S)) then
       R:= R,k+1; count:= count+1;
  fi
od:
R; # Robert Israel, Oct 25 2019

Mathematica

a = {}; Do[If[Sqrt[Denominator[Sum[1/x^2, {x, 1, Prime[x] - 1}]]] == Floor[Sqrt[Denominator[Sum[1/x^2, {x, 1, Prime[x] - 1}]]]], 1,AppendTo[a, Prime[x]]], {x, 1, 50}]; a

Extensions

More terms from Robert Israel, Oct 25 2019