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 A035216 #9 Nov 19 2023 01:25:02 %S A035216 1,1,2,1,2,2,0,1,3,2,2,2,0,0,4,1,1,3,0,2,0,2,0,2,3,0,4,0,2,4,0,1,4,1, %T A035216 0,3,2,0,0,2,0,0,0,2,6,0,2,2,1,3,2,0,0,4,4,0,0,2,0,4,2,0,0,1,0,4,0,1, %U A035216 0,0,0,3,0,2,6,0,0,0,0,2,5 %N A035216 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 34. %H A035216 Amiram Eldar, <a href="/A035216/b035216.txt">Table of n, a(n) for n = 1..10000</a> %F A035216 From _Amiram Eldar_, Nov 19 2023: (Start) %F A035216 a(n) = Sum_{d|n} Kronecker(34, d). %F A035216 Multiplicative with a(p^e) = 1 if Kronecker(34, p) = 0 (p = 2 or 17), a(p^e) = (1+(-1)^e)/2 if Kronecker(34, p) = -1 (p is in A038910), and a(p^e) = e+1 if Kronecker(34, p) = 1 (p is in A191025). %F A035216 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(6*sqrt(34)+35)/sqrt(34) = 1.457151825131... . (End) %t A035216 a[n_] := DivisorSum[n, KroneckerSymbol[34, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 19 2023 *) %o A035216 (PARI) my(m = 34); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X)) %o A035216 (PARI) a(n) = sumdiv(n, d, kronecker(34, d)); \\ _Amiram Eldar_, Nov 19 2023 %Y A035216 Cf. A038910, A191025. %K A035216 nonn,easy,mult %O A035216 1,3 %A A035216 _N. J. A. Sloane_