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 A307623 #27 May 29 2019 19:03:55
%S A307623 1,4,12,18,46,102,108,124,126,148,246,468,1002,1008,1014,1022,1023,
%T A307623 1025,1026,1068,1234,1236,1245,1248,1268,1458,2456,2468,10023,10025,
%U A307623 10026,10068,10124,10125,10146,10224,10234,10236,10245,10248,10458,12345,12348,12369
%N A307623 Numbers that set a record for the number of distinct composite numbers that can be obtained by permuting some subset of their digits.
%H A307623 Daniel Lignon, <a href="/A307623/b307623.txt">Table of n, a(n) for n = 1..74</a>
%e A307623 108 is in this sequence because the number of composite numbers which can be obtained by permuting some or all of digits of 108 is larger than the number of composite numbers obtainable in the same way for any smaller integer. With 108, you can form 9 composite numbers: 8, 10, 18, 80, 81, 108, 180, 801, 810. It's impossible to form n >= 9 composite numbers in the same way with any integer < 108.
%t A307623 f[n_] := Length[Union[ Select[FromDigits /@ Flatten[Permutations /@ Subsets[IntegerDigits[n]], 1], CompositeQ]]];
%t A307623 d=-1; res={};Do[b=f[n];If[b>d,AppendTo[res,n];d=b],{n,10000}];res
%Y A307623 Cf. A072857 (the same with primes instead of composite numbers) and A307624.
%K A307623 nonn,base
%O A307623 1,2
%A A307623 _Daniel Lignon_, Apr 19 2019