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 A333702 #20 Feb 23 2024 21:40:08
%S A333702 1,2,10,22,25,29,33,70,118,358,598,1438,1803,1819,2878,2881,2997,4318,
%T A333702 4322,4388,10078,20158,21967,21971,21975,30238,30241,30837,40318,
%U A333702 120958,141121,142557,201598,214563,214675,282238,362878,649446,649504,1088638,1303204,1303314
%N A333702 Numbers k such that k divides the sum of digits in factorial base of all numbers from 1 to k.
%C A333702 The corresponding quotients are 1, 1, 2, 3, 3, 3, 3, 4, 5, ...
%H A333702 Amiram Eldar, <a href="/A333702/b333702.txt">Table of n, a(n) for n = 1..137</a>
%H A333702 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e A333702 10 is a term since the sum of digits in factorial base (A034968) of k from 1 to 10 is 1 + 1 + 2 + 2 + 3 + 1 + 2 + 2 + 3 + 3 = 20, which is divisible by 10.
%t A333702 f[n_] := Module[{s=0, i=2, k=n}, While[k > 0, k = Floor[n/i!]; s = s + (i-1)*k; i++]; n-s]; seq = {}; s = 0; Do[s += f[n]; If[Divisible[s, n], AppendTo[seq, n]], {n, 1, 10^5}]; seq (* after _Jean-François Alcover_ at A034968 *)
%Y A333702 Cf. A007623, A034968, A368342.
%Y A333702 Cf. A095376, A114136, A333703, A333704, A333705.
%K A333702 nonn,base
%O A333702 1,2
%A A333702 _Amiram Eldar_, Apr 02 2020