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 A138570 #9 Jun 09 2022 19:32:58
%S A138570 1,2,6,12,60,120,840,2520,27720,55440,720720,1081080,2162160,36756720,
%T A138570 698377680,16062686640,48188059920,160626866400,240940299600,
%U A138570 6987268688400,216605329340400,288807105787200,1010824870255200
%N A138570 Numbers that set records for the number by which they must be multiplied to double the number of divisors.
%C A138570 A number is in this sequence exactly once if and only if it is in A135060 at least once.
%H A138570 Ray Chandler, <a href="/A138570/b138570.txt">Table of n, a(n) for n = 1..52</a>
%e A138570 840 is a term of this sequence because 840 sets a new record (9) for the number by which it must be multiplied to double its number of divisors (840 has 32 divisors; the smallest number with 64 divisors is 840 * 9 = 7560).
%e A138570 120's record of 7 is not exceeded by any number from 121 to 839.
%t A138570 f[ n_ ] := f[ n ] = Module[ {i = 2}, While[ 2 * Length[ Divisors[ n ] ] != Length[ Divisors[ i * n ] ], i++ ]; Return[ i ] ]; A138570 = {}; searchMax = 100000; currHigh = 0; i = 1; While[ i < searchMax, n = f[ i ]; If[ n > currHigh, A138570 = {A138570, i}; currHigh = n ]; i++ ]; A138570 = Flatten[ A138570 ]
%Y A138570 Cf. A135060.
%K A138570 nonn
%O A138570 1,2
%A A138570 _J. Lowell_, May 12 2008
%E A138570 a(1) to a(8) verified and a(9) to a(12) added by _Alonso del Arte_, Oct 25 2009
%E A138570 Extended by _Ray Chandler_, Nov 10 2009