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 A358176 #13 Jan 16 2023 09:10:46
%S A358176 1,2,3,4,7,6,8,5,9,13,10,12,14,15,16,31,18,21,20,22,24,25,62,26,27,28,
%T A358176 30,32,33,34,36,35,38,39,40,42,44,45,46,48,50,51,52,49,19,54,55,56,57,
%U A358176 58,60,63,64,127,66,68,69,70,72,65,74,75,76,77,78,80,81,11,82,84,86,87,85,88,90,91,92
%N A358176 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with sigma(a(n-1)).
%C A358176 The sequence is conjectured to be a permutation of the positive integers. In the first 500000 terms the fixed points are 1, 2, 3, 4, 6, 9, 12. It is unlikely more exist although this is unknown.
%H A358176 Michael De Vlieger, <a href="/A358176/b358176.txt">Table of n, a(n) for n = 1..10000</a>
%H A358176 Scott R. Shannon, <a href="/A358176/a358176.png">Image of the first 200000 terms</a>. The green line is a(n) = n.
%H A358176 Michael De Vlieger, <a href="/A358176/a358176_1.png">Annotated log-log scatterplot of a(n)</a>, n = 1..2^14, showing records in red and local minima in blue, highlighting primes in green and other prime powers in gold. Extreme records and local minima are labeled in red and blue respectively, and composite prime powers in orange.
%e A358176 a(8) = 5 as a(7) = 8 and sigma(8) = A000203(8) = 15, and 5 is the smallest unused number that shares a factor with 15.
%t A358176 nn = 120; c[_] = False; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; u = 3; Do[Set[{k, s}, {u, DivisorSigma[1, a[n - 1]]}]; While[Or[c[k], CoprimeQ[s, k]], k++]; Set[{a[n], c[k]}, {k, True}]; If[k == u, While[c[u], u++]], {n, 3, nn}]; Array[a, nn] (* _Michael De Vlieger_, Nov 05 2022 *)
%Y A358176 Cf. A000203, A358082, A358201, A064413, A356851, A356430, A354960.
%K A358176 nonn
%O A358176 1,2
%A A358176 _Scott R. Shannon_, Nov 02 2022