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A166405 Sum of those positive i <= 2n+1, for which J(i,2n+1)=-1. Here J(i,k) is the Jacobi symbol.

%I A166405 #13 Dec 13 2023 18:29:18
%S A166405 0,2,5,14,0,33,39,45,68,95,63,161,0,126,203,279,165,245,333,312,410,
%T A166405 473,270,658,0,459,689,660,513,944,915,630,780,1139,759,1491,1314,775,
%U A166405 1155,1738,0,1826,1360,1479,1958,1729,1395,2090,2328,1485,2525,2884
%N A166405 Sum of those positive i <= 2n+1, for which J(i,2n+1)=-1. Here J(i,k) is the Jacobi symbol.
%H A166405 A. Karttunen, <a href="/A166405/b166405.txt">Table of n, a(n) for n = 0..131071</a>
%e A166405 For n=5, we get odd number 11 (2*5+1), and J(i,11) = 1,-1,1,1,1,-1,-1,-1,1,-1,0 when i ranges from 1 to 11, J(i,11) obtaining value -1 when i=2, 6, 7, 8 and 10, thus a(5)=33.
%t A166405 Table[Total@ Select[Range[2n + 1], JacobiSymbol[#, 2n + 1]==-1 &], {n, 0, 100}] (* _Indranil Ghosh_, Jun 12 2017 *)
%o A166405 (MIT/GNU Scheme)
%o A166405 (define (A166405 n) (let ((w (A005408 n))) (let loop ((i 1) (s 0)) (cond ((= i w) s) (else (loop (1+ i) (+ s (if (= -1 (jacobi-symbol (1+ i) w)) (1+ i) 0))))))))
%o A166405 (Python)
%o A166405 from sympy import jacobi_symbol as J
%o A166405 def a(n): return sum(i for i in range(1, 2*n + 2) if J(i, 2*n + 1)==-1)
%o A166405 # _Indranil Ghosh_, Jun 12 2017
%Y A166405 A125615(n)=a(A102781(n)). Cf. A166100, A166406-A166408. The cases where a(i)/A005408(i) is not integer seem also to be given by A166101. This is NOT a bisection of A165898. Scheme-code for jacobi-symbol is given at A165601.
%K A166405 nonn
%O A166405 0,2
%A A166405 _Antti Karttunen_, Oct 21 2009