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 A362681 #38 May 09 2023 22:29:07
%S A362681 0,0,1,1,2,1,3,1,1,1,2,1,3,1,1,1,2,1,3,1,1,3,2,1,2,4,1,1,2,1,3,1,1,3,
%T A362681 1,1,2,4,1,1,2,1,3,1,1,3,2,1,5,1,1,1,2,1,3,1,1,3,2,1,3,3,1,1,2,1,3,2,
%U A362681 1,1,2,1,3,4,1,3,2,1,3,1,1,2,2,1,3,3,1,1
%N A362681 The number of steps, starting from n, to reach x<=2 in an iteration x <- 2x - {sum of proper factors of 2x}.
%C A362681 A proper factor is defined as any divisor of n other than 1 and itself (Derbyshire).
%C A362681 The iteration step is x <- A157449(2x).
%C A362681 The iteration ends on the step after reaching half of any abundant number A005101/2.
%C A362681 a(1682)=7 is the only number over 6 in the first 10^6 terms.
%C A362681 Powers of 2 reach 2 in the first step, and then would enter an infinite loop if the iteration ended only when x <= 1.
%D A362681 J. Derbyshire, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Penguin, 2004, p. 32.
%H A362681 Christian N. K. Anderson, <a href="/A362681/b362681.txt">Table of n, a(n) for n = 1..10000</a>
%H A362681 Christian N. K. Anderson, <a href="/A362681/a362681.pdf">Graph showing sparsity of 6s</a>
%o A362681 (PARI) a(n) = my(ret=0); while(n>2, n = 4*n+1-sigma(2*n); ret++); ret; \\ _Kevin Ryde_, May 09 2023
%Y A362681 Cf. A157449, A005101, A362684 (indices of records).
%K A362681 nonn,easy
%O A362681 1,5
%A A362681 _Kevin L. Schwartz_ and _Christian N. K. Anderson_, May 01 2023