This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A035194 #19 Nov 18 2023 06:30:31
%S A035194 1,1,1,1,0,1,0,1,1,0,2,1,2,0,0,1,0,1,0,0,0,2,2,1,1,2,1,0,0,0,0,1,2,0,
%T A035194 0,1,2,0,2,0,0,0,0,2,0,2,2,1,1,1,0,2,0,1,0,0,0,0,2,0,2,0,0,1,0,2,0,0,
%U A035194 2,0,2,1,2,2,1,0,0,2,0,0,1
%N A035194 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 12.
%C A035194 Coefficients of Dedekind zeta function for the quadratic number field of discriminant 12. See A002324 for formula and Maple code. - _N. J. A. Sloane_, Mar 22 2022
%H A035194 G. C. Greubel, <a href="/A035194/b035194.txt">Table of n, a(n) for n = 1..10000</a>
%F A035194 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(2+sqrt(3))/sqrt(3) = 0.760345... (A196530). - _Amiram Eldar_, Oct 11 2022
%F A035194 From _Amiram Eldar_, Nov 18 2023: (Start)
%F A035194 a(n) = Sum_{d|n} Kronecker(12, d).
%F A035194 Multiplicative with a(p^e) = 1 if Kronecker(12, p) = 0 (p = 2 or 3), a(p^e) = (1+(-1)^e)/2 if Kronecker(12, p) = -1 (p is in A003630), and a(p^e) = e+1 if Kronecker(12, p) = 1 (p is in A097933). (End)
%t A035194 a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[12, #] &]]; Table[ a[n], {n, 1, 100}] (* _G. C. Greubel_, Apr 27 2018 *)
%o A035194 (PARI) my(m=12); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o A035194 (PARI) a(n) = sumdiv(n, d, kronecker(12, d)); \\ _Amiram Eldar_, Nov 18 2023
%Y A035194 Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
%Y A035194 Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
%Y A035194 Cf. A003630, A097933, A196530.
%K A035194 nonn,easy,mult
%O A035194 1,11
%A A035194 _N. J. A. Sloane_