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 A346729 #22 Aug 08 2021 11:39:15
%S A346729 1,2,4,6,8,12,16,20,24,32,40,48,64,80,96,120,144,168,200,240,288,360,
%T A346729 432,504,600,720,864,1008,1152,1344,1600,1920,2304,2688,3072,3584,
%U A346729 4096,4800,5760,6720,7680,8640,10080,11520,13824,16128,18432,20736,23040,27648
%N A346729 Maximum number of divisors among n-bit numbers.
%C A346729 a(n) is the maximum value of tau(k)=A000005(k) for k in the interval [2^(n-1), 2^n - 1]. For n >= 3, that smallest k at which tau(k) is maximized in that interval is A036484(n).
%C A346729 No term is repeated: for n >= 1, if k is the number in [2^(n-1), 2^n - 1] at which tau(k) is maximized (i.e., tau(k) = a(n)), then 2k, which will be a number in [2^n, 2^(n+1) - 1], will have more divisors than k has, so a(n+1) >= tau(2k) > tau(k) = a(n).
%e A346729 There are four 3-bit numbers: 4 = 100_2, 5 = 101_2 = 5, 6 = 110_2, 7 = 111_2. 5 and 7 are both prime, so each has 2 divisors; 4 = 2^2 has 3 divisors (1, 2, and 4), and 6 = 2*3 has 4 divisors (1, 2, 3, and 6). Thus, the maximum number of divisors among 3-bit numbers is A000005(6) = 4, so a(3)=4.
%t A346729 a[n_]:=Max[Table[DivisorSigma[0,k],{k,2^(n-1),2^n-1}]]; Table[a[n],{n,23}] (* _Stefano Spezia_, Aug 02 2021 *)
%o A346729 (Python)
%o A346729 from sympy import divisors
%o A346729 def a(n): return max(len(divisors(n)) for n in range(2**(n-1), 2**n))
%o A346729 print([a(n) for n in range(1, 18)]) # _Michael S. Branicky_, Aug 02 2021
%o A346729 (PARI) a(n) = vecmax(apply(numdiv, [2^(n-1)..2^n-1])); \\ _Michel Marcus_, Aug 03 2021
%Y A346729 Cf. A000005, A002183, A036484, A346730.
%K A346729 nonn
%O A346729 1,2
%A A346729 _Jon E. Schoenfield_, Jul 30 2021