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 A356430 #7 Jan 16 2023 09:10:46 %S A356430 1,2,4,3,6,8,10,12,9,15,14,16,5,18,20,21,22,24,26,28,27,30,32,33,34, %T A356430 36,39,38,40,42,44,45,46,48,25,51,50,52,54,56,58,60,57,62,64,7,66,68, %U A356430 63,69,70,72,74,76,75,78,80,35,82,84,81,55,86,88,90,87,92,93,94,96,98,99,100,102,104 %N A356430 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with the number of divisors of a(n-1). %C A356430 The sequence is conjectured to be a permutation of the positive integers although it may take a large number of terms for the primes to appear, e.g., 19 has not occurred after 100000 terms. In the same range the only fixed points are 1, 2, and 9, and it is likely no more exist. %H A356430 Scott R. Shannon, <a href="/A356430/a356430.png">Image of the first 1000 terms</a>. The green line is y = n. %e A356430 a(9) = 9 as a(8) = 12 which has six divisors, and 9 is the smallest unused number that shares a factor with 6. %Y A356430 Cf. A356431, A356432, A000005, A354960, A348086. %K A356430 nonn %O A356430 1,2 %A A356430 _Scott R. Shannon_, Aug 07 2022