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 A035201 #9 Nov 19 2023 01:29:17 %S A035201 1,0,2,1,2,0,0,0,3,0,0,2,0,0,4,1,2,0,1,2,0,0,0,0,3,0,4,0,0,0,2,0,0,0, %T A035201 0,3,0,0,0,0,0,0,0,0,6,0,0,2,1,0,4,0,0,0,0,0,2,0,2,4,2,0,0,1,0,0,2,2, %U A035201 0,0,2,0,2,0,6,1,0,0,2,2,5 %N A035201 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 19. %H A035201 Amiram Eldar, <a href="/A035201/b035201.txt">Table of n, a(n) for n = 1..10000</a> %F A035201 From _Amiram Eldar_, Nov 19 2023: (Start) %F A035201 a(n) = Sum_{d|n} Kronecker(19, d). %F A035201 Multiplicative with a(19^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(19, p) = -1 (p is in A038892), and a(p^e) = e+1 if Kronecker(19, p) = 1 (p is in A297175). %F A035201 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(39*sqrt(19)+170)/(3*sqrt(19)) = 0.891499901309... . (End) %t A035201 a[n_] := DivisorSum[n, KroneckerSymbol[19, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 19 2023 *) %o A035201 (PARI) my(m = 19); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X)) %o A035201 (PARI) a(n) = sumdiv(n, d, kronecker(19, d)); \\ _Amiram Eldar_, Nov 19 2023 %Y A035201 Cf. A038892, A297175. %K A035201 nonn,easy,mult %O A035201 1,3 %A A035201 _N. J. A. Sloane_