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 A349223 #15 Nov 12 2021 04:36:40
%S A349223 1,4,16,36,64,96,144,240,288,360,432,480,576,720,864,960,1152,1440,
%T A349223 2160,2880,4320,5040,5760,7200,8640,10080,11520,12960,14400,15120,
%U A349223 17280,20160,25920,28800,30240,34560,40320,50400,51840,60480,80640,86400,90720,100800,120960
%N A349223 Numbers k with a record number of ways to factor k into composite factors.
%C A349223 Except for the term 4, the indices of records of A050370.
%C A349223 The corresponding record values are 0, 1, 2, 3, 4, 5, 8, 9, 11, 12, 13, 14, ... (see the link for more values).
%H A349223 Amiram Eldar, <a href="/A349223/b349223.txt">Table of n, a(n) for n = 1..200</a>
%H A349223 Amiram Eldar, <a href="/A349223/a349223.txt">Table of n, a(n) and record values for n = 1..200</a>
%e A349223 a(1) = 1 since 1 has 0 ways to be factored into composite factors.
%e A349223 a(2) = 4 since 4 is composite and has 1 presentation as a product of composite numbers: 4.
%e A349223 a(3) = 16 since 16 has 2 presentations as a product of composite numbers: 4 * 4 and 16.
%e A349223 a(4) = 36 since 36 has 3 presentations as a product of composite numbers: 6 * 6, 4 * 9 and 36.
%t A349223 f[_, 1] = f[1, _] = 1; f[n_, m_] := f[n, m] = DivisorSum[n, f[n/#, #] &, 1 < # <= m &]; g[n_] := DivisorSum[n, MoebiusMu[n/#]*f[#, #] &]; gm = 0; seq = {1}; Do[g1 = g[n]; If[g1 > gm, gm = g1; AppendTo[seq, n]], {n, 2, 10^5}]; seq
%Y A349223 Cf. A002808, A050370.
%Y A349223 Subsequence of A025487.
%K A349223 nonn
%O A349223 1,2
%A A349223 _Amiram Eldar_, Nov 11 2021