cp's OEIS Frontend

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.

A035226 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = 44.

This page as a plain text file.
%I A035226 #10 Nov 20 2023 11:40:46
%S A035226 1,1,0,1,2,0,2,1,1,2,1,0,0,2,0,1,0,1,2,2,0,1,0,0,3,0,0,2,0,0,0,1,0,0,
%T A035226 4,1,2,2,0,2,0,0,2,1,2,0,0,0,3,3,0,0,2,0,2,2,0,0,0,0,0,0,2,1,0,0,0,0,
%U A035226 0,4,0,1,0,2,0,2,2,0,2,2,1
%N A035226 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = 44.
%H A035226 Amiram Eldar, <a href="/A035226/b035226.txt">Table of n, a(n) for n = 1..10000</a>
%F A035226 From _Amiram Eldar_, Nov 20 2023: (Start)
%F A035226 a(n) = Sum_{d|n} Kronecker(44, d).
%F A035226 Multiplicative with a(p^e) = 1 if Kronecker(44, p) = 0 (p = 2 or 11), a(p^e) = (1+(-1)^e)/2 if Kronecker(44, p) = -1 (p is in A296936), and a(p^e) = e+1 if Kronecker(44, p) = 1 (p is in A296935).
%F A035226 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(3*sqrt(11)+10)/sqrt(44) = 0.902490644956... . (End)
%t A035226 a[n_] := DivisorSum[n, KroneckerSymbol[44, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 20 2023 *)
%o A035226 (PARI) my(m = 44); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o A035226 (PARI) a(n) = sumdiv(n, d, kronecker(44, d)); \\ _Amiram Eldar_, Nov 20 2023
%Y A035226 Cf. A296935, A296936.
%K A035226 nonn,easy,mult
%O A035226 1,5
%A A035226 _N. J. A. Sloane_