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%I #31 Nov 20 2017 23:20:55
%S -1,3,1,-5,-1,5,7,-5,-3,5,9,-1,3,-7,-11,7,11,-13,-9,-7,-1,15,13,-15,1,
%T -13,-9,5,-17,13,11,9,-5,17,7,-17,19,1,-3,15,17,-7,21,19,-5,-11,-21,
%U 19,13,1,-23,5,-17,-19,25,-13,-25,-23,-1,-5,15,27,-9,-19,25,-17,11,5,-25,27,23,29,-29,25
%N a(n) = A002172(n) / 2.
%H Seiichi Manyama, <a href="/A046730/b046730.txt">Table of n, a(n) for n = 1..10000</a>
%H L. Carlitz, <a href="http://dx.doi.org/10.1090/S0025-5718-1962-0152678-2">The coefficients of the lemniscate function</a>, Math. Comp., 16 (1962), 475-478.
%H <a href="/index/Ge#Glaisher">Index entries for sequences related to Glaisher's numbers</a>
%e From _Seiichi Manyama_, Sep 26 2016: (Start)
%e Let p be a prime of the form 4k+1 so that p = a^2 + b^2.
%e We take a odd and such that a = b + 1 (mod 4).
%e p = 5 = (-1)^2 + 2^2 and -1 = 2 + 1 (mod 4). So a(1) = -1.
%e p = 13 = 3^2 + 2^2 and 3 = 2 + 1 (mod 4). So a(2) = 3.
%e p = 17 = 1^2 + 4^2 and 1 = 4 + 1 (mod 4). So a(3) = 1.
%e p = 29 = 5^2 + 2^2 and -5 = 2 + 1 (mod 4). So a(4) = -5.
%e (End)
%t Map[-Sum[JacobiSymbol[x^3 - x, #], {x, 0, # - 1}] &, Select[Prime@ Range@ 155, Mod[#, 4] == 1 &]]/2 (* _Michael De Vlieger_, Sep 26 2016, after _Jean-François Alcover_ at A002172 *)
%o (PARI) a002172(n) = {my(m, c); if(n<1, 0, c=0; m=0; while(c<n, m++; if(isprime(m)& m%4==1, c++)); -sum(x=0, m-1, kronecker(x^3-x, m)))}
%o a(n) = a002172(n)/2; \\ _Altug Alkan_, Sep 27 2016
%Y Cf. A002172.
%K sign
%O 1,2
%A _N. J. A. Sloane_
%E Offset changed to 1 to match A002172, _Joerg Arndt_, Sep 27 2016
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