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 A035193 #12 Nov 18 2023 06:30:28 %S A035193 1,0,0,1,2,0,2,0,1,0,1,0,0,0,0,1,0,0,2,2,0,0,0,0,3,0,0,2,0,0,0,0,0,0, %T A035193 4,1,2,0,0,0,0,0,2,1,2,0,0,0,3,0,0,0,2,0,2,0,0,0,0,0,0,0,2,1,0,0,0,0, %U A035193 0,0,0,0,0,0,0,2,2,0,2,2,1 %N A035193 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 11. %H A035193 G. C. Greubel, <a href="/A035193/b035193.txt">Table of n, a(n) for n = 1..10000</a> %F A035193 From _Amiram Eldar_, Nov 18 2023: (Start) %F A035193 a(n) = Sum_{d|n} Kronecker(11, d). %F A035193 Multiplicative with a(11^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(11, p) = -1 (p is in A296936), and a(p^e) = e+1 if Kronecker(11, p) = 1 (p is in A296935). %F A035193 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(3*sqrt(11)+10)/(3*sqrt(11)) = 0.60166042997... . (End) %t A035193 a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[11, #] &]]; Table[ a[n], {n, 1, 100}] (* _G. C. Greubel_, Apr 27 2018 *) %o A035193 (PARI) my(m=11); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X)) %o A035193 (PARI) a(n) = sumdiv(n, d, kronecker(11, d)); \\ _Amiram Eldar_, Nov 18 2023 %Y A035193 Cf. A296935, A296936. %K A035193 nonn,easy,mult %O A035193 1,5 %A A035193 _N. J. A. Sloane_