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 A035160 #16 Jul 08 2025 21:30:56 %S A035160 1,1,1,1,1,1,0,1,1,1,2,1,2,0,1,1,2,1,0,1,0,2,2,1,1,2,1,0,2,1,2,1,2,2, %T A035160 0,1,2,0,2,1,0,0,2,2,1,2,2,1,1,1,2,2,0,1,2,0,0,2,2,1,0,2,0,1,2,2,2,2, %U A035160 2,0,0,1,0,2,1,0,0,2,2,1,1 %N A035160 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -30. %H A035160 Amiram Eldar, <a href="/A035160/b035160.txt">Table of n, a(n) for n = 1..10000</a> %F A035160 From _Amiram Eldar_, Nov 17 2023: (Start) %F A035160 a(n) = Sum_{d|n} Kronecker(-30, d). %F A035160 Multiplicative with a(p^e) = 1 if Kronecker(-30, p) = 0 (p = 2, 3 or 5), a(p^e) = (1+(-1)^e)/2 if Kronecker(-30, p) = -1 (p is in A191066), and a(p^e) = e+1 if Kronecker(-30, p) = 1 (p is in A191023). %F A035160 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/sqrt(30) = 1.1471474... . (End) %t A035160 a[n_] := DivisorSum[n, KroneckerSymbol[-30, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 17 2023 *) %o A035160 (PARI) my(m = -30); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X)) %o A035160 (PARI) a(n) = sumdiv(n, d, kronecker(-30, d)); \\ _Amiram Eldar_, Nov 17 2023 %Y A035160 Cf. A191023, A191066. %K A035160 nonn,easy,mult %O A035160 1,11 %A A035160 _N. J. A. Sloane_