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 A333849 #14 Oct 15 2020 16:36:30
%S A333849 2,1,2,1,1,1,2,2,2,1,6,1,2,1,2,1,2,2,2,6,2,1,2,1,1,2,2,10,6,1,2,6,2,1,
%T A333849 2,1,2,2,2,1,1,1,2,2,2,2,6,2,2,2,2,1,6,1,2,6,2,2,6,2,1,2,2,1,6,1,2,2,
%U A333849 2,1,2,2,2,6,2,1,2,10,2,2,2,1,10,1,2,18,2,2,2,1,2
%N A333849 a(n) = gcd(A333848(n), 2*(2*n+1)), for n >= 0.
%C A333849 For n >= 1, a(n) enters the formula for the length L(2*n+1) = A332441(n) of the directed Euler tour ET(2*n+1, q0 = 1) based on the unsigned Schick sequence for 2*n+1, namely L(2*n+1) = A003558(n)*2*(2*n+1)/a(n). For Schick sequences and references see A332439.
%H A333849 Michael De Vlieger, <a href="/A333849/b333849.txt">Table of n, a(n) for n = 0..10000</a>
%H A333849 Wolfdieter Lang, <a href="https://arxiv.org/abs/2008.04300">On the Equivalence of Three Complete Cyclic Systems of Integers</a>, arXiv:2008.04300 [math.NT], 2020.
%F A333849 a(n) = gcd(A333848(n), 2*(2*n+1)), for n >= 0.
%t A333849 {2}~Join~Table[GCD[Total@ Select[Range[1, m, 2], GCD[#, m] == 1 &], 2 m], {m, Array[2 # + 1 &, 85]}] (* _Michael De Vlieger_, Oct 15 2020 *)
%o A333849 (PARI) f(n) = if (n==0, 0, my(m=2*n+1); vecsum(select(x->((gcd(m, x)==1) && (x%2)), [1..m]))); \\ A333848
%o A333849 a(n) = gcd(f(n), 2*(2*n+1)); \\ _Michel Marcus_, May 05 2020
%Y A333849 Cf. A003558, A332439, A332441, A333848.
%K A333849 nonn,easy
%O A333849 0,1
%A A333849 _Wolfdieter Lang_, May 01 2020