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(Sum of the quadratic residues of prime(n)) / prime(n).
10

%I #9 Feb 25 2015 23:32:42

%S 1,1,2,3,4,4,4,7,6,9,10,10,9,13,13,15,16,14,18,17,19,22,24,25,23,25,

%T 27,28,29,30,34,33,37,34,39,40,36,43,42,45,41,48,49,45,51,52,54,57,58,

%U 52,60,59,64,59,67,62,69,70,69,73,75,68,78,79,81,84,84,87,88,80,87,93,93

%N (Sum of the quadratic residues of prime(n)) / prime(n).

%C Always an integer for primes > 3.

%D Kenneth A. Ribet, Modular forms and Diophantine questions, Challenges for the 21st century (Singapore 2000), 162-182; World Sci. Publishing, River Edge NJ 2001; Math. Rev. 2002i:11030.

%F a(n) = A076409(n)/prime(n).

%F a(n) ~= p(n)/4. - _David W. Wilson_, Oct 09 2002

%F If prime(n) = 4k+1 then a(n) = k.

%t Table[ Apply[ Plus, Flatten[ Position[ Table[ JacobiSymbol[i, Prime[n]], {i, 1, Prime[n] - 1}], 1]]] /Prime[n], {n, 3, 50}]

%K nonn

%O 3,3

%A _R. K. Guy_, Oct 08 2002

%E Edited and extended by _Robert G. Wilson v_, Oct 09 2002