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 A035200 #10 Nov 19 2023 01:26:47 %S A035200 1,1,1,1,0,1,2,1,1,0,0,1,0,2,0,1,2,1,0,0,2,0,2,1,1,0,1,2,0,0,2,1,0,2, %T A035200 0,1,0,0,0,0,2,2,0,0,0,2,2,1,3,1,2,0,0,1,0,2,0,0,0,0,0,2,2,1,0,0,0,2, %U A035200 2,0,2,1,2,0,1,0,0,0,2,0,1 %N A035200 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 18. %H A035200 Amiram Eldar, <a href="/A035200/b035200.txt">Table of n, a(n) for n = 1..10000</a> %F A035200 From _Amiram Eldar_, Nov 19 2023: (Start) %F A035200 a(n) = Sum_{d|n} Kronecker(18, d). %F A035200 Multiplicative with a(p^e) = 1 if Kronecker(18, p) = 0 (p = 2 or 3), a(p^e) = (1+(-1)^e)/2 if Kronecker(18, p) = -1 (p is in A003629 \ {3}), and a(p^e) = e+1 if Kronecker(18, p) = 1 (p is in A001132). %F A035200 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4*log(sqrt(2)+1)/(3*sqrt(2)) = 0.830966986853... . (End) %t A035200 a[n_] := DivisorSum[n, KroneckerSymbol[18, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 19 2023 *) %o A035200 (PARI) my(m = 18); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X)) %o A035200 (PARI) a(n) = sumdiv(n, d, kronecker(18, d)); \\ _Amiram Eldar_, Nov 19 2023 %Y A035200 Cf. A001132, A003629. %K A035200 nonn,easy,mult %O A035200 1,7 %A A035200 _N. J. A. Sloane_