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 A335832 #18 Jul 18 2024 09:18:43
%S A335832 1,4,16,144,256,1296,2304,20736,518400,1679616,5308416,12960000,
%T A335832 41990400,132710400,429981696,635040000,1049760000,3317760000,
%U A335832 10749542400,31116960000,51438240000,162570240000,268738560000,2520473760000,7965941760000,13168189440000,167961600000000
%N A335832 Numbers k with record values of the ratio d(k)/id(k) between the number of divisors and the number of infinitary divisors.
%C A335832 This sequence is infinite since the ratio d(k)/id(k) is unbounded. For example, for k = 2^(2^m) we have d(k)/id(k) = (2^m+1)/2.
%C A335832 The corresponding record values are 1, 1.5, 2.5, 3.75, 4.5, 6.25, 6.75, 11.25, 16.875, 20.25, ...
%H A335832 Amiram Eldar, <a href="/A335832/b335832.txt">Table of n, a(n) for n = 1..96</a>
%F A335832 The ratios d(k)/id(k) for k = 1, 2, 3 and 4 are 1, 1, 1 and 3/2. The record values occur at 1 and 4.
%t A335832 id[1] = 1; id[n_] := Times @@ Flatten[2^DigitCount[#, 2, 1] & /@ FactorInteger[n][[All, 2]]]; f[1] = 1; f[n_] := DivisorSigma[0, n]/id[n]; seq = {}; fm = 0; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[seq, n]], {n, 1, 10^6}]; seq
%Y A335832 Subsequence of A025487.
%Y A335832 Cf. A000005, A037445, A307870.
%K A335832 nonn
%O A335832 1,2
%A A335832 _Amiram Eldar_, Jun 25 2020