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 A027414 #15 Jul 08 2025 17:51:45
%S A027414 1,2,1,2,0,1,1,2,2,2,1,1,0,1,0,2,2,3,1,2,0,1,1,1,1,2,2,1,0,0,1,2,2,4,
%T A027414 0,3,0,1,0,2,2,0,1,1,0,1,1,1,2,4,2,2,0,2,0,1,2,2,1,0,0,1,1,2,0,2,1,4,
%U A027414 0,0,1,3,2,2,1,1,0,0,1,2,3,4,1,0,0,1,0,1,2,2,0,1,0,1,0,1,2,3,3,4,0,2,1,2,0
%N A027414 G.f. for Moebius transform is x * (1 + x) / (1 + x^4).
%H A027414 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A027414 Moebius transform is period 8 sequence [1, 1, 0, 0, -1, -1, 0, 0, ...]. - _Michael Somos_, Sep 20 2005
%F A027414 G.f.: Sum_{k>0} x^k * (1 + x^k) / (1 + x^(4*k)). - _Michael Somos_, Sep 20 2005
%F A027414 a(8*n + 5) = 0. a(8*n + 3) = A033761(n). - _Michael Somos_, Nov 16 2011
%e A027414 x + 2*x^2 + x^3 + 2*x^4 + x^6 + x^7 + 2*x^8 + 2*x^9 + 2*x^10 + x^11 + x^12 + ...
%t A027414 a[ n_] := If[ n < 1, 0, Sum[ {1, 1, 0, 0, -1, -1, 0, 0} [[ Mod[d, 8, 1]]], {d, Divisors @ n}]] (* _Michael Somos_, Nov 16 2011 *)
%o A027414 (PARI) {a(n) = if( n<1, 0, sumdiv( n, d, kronecker( -4, (d-1)%8\2 + 1)))} /* _Michael Somos_, Sep 20 2005 */
%K A027414 nonn
%O A027414 1,2
%A A027414 _N. J. A. Sloane_