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 A341435 #6 Feb 11 2021 22:58:39
%S A341435 1,3,6,8,12,16,24,36,48,72,96,120,144,216,288,432,576,720,864,1080,
%T A341435 1152,1440,2016,2160,2880,3600,4320,5040,5760,6480,7200,8640,10080,
%U A341435 10800,14400,20160,21600,25920,28800,32400,40320,43200,50400,64800,86400,100800,129600
%N A341435 Numbers k that are divisible by their product of digits in a record number of bases 1 < b < k.
%C A341435 The corresponding record values are 0, 1, 2, 3, 5, 6, 9, 12, 15, 20, 22, 23, 32, 35, 46, 52, 58, 68, 69, 71, 76, 95, 96, 106, 126, 137, 145, 149, 161, 164, 185, 191, 196, 218, 249, 266, 286, 290, 310, 318, 330, 375, 387, 428, 471, 510, 564, ...
%C A341435 It seems that most terms are least integers of a prime signature (A025487), but some are not: e.g., 3 and 2016.
%e A341435 The values of A341434(k) for k=1..8 are 0, 0, 1, 1, 1, 2, 2, 3. The record values, 0, 1, 2 and 3, occur at 1, 3, 6 and 8, the first 4 terms of this sequence.
%t A341435 q[n_, b_] := (p = Times @@ IntegerDigits[n, b]) > 0 && Divisible[n, p]; a[n_] := Count[Range[2, n], _?(q[n, #] &)]; s = {}; am = -1; Do[a1 = a[n]; If[a1 > am, am = a1; AppendTo[s, n]], {n, 1, 10^3}]; s
%Y A341435 Indices of records in A341434.
%Y A341435 Cf. A330813.
%K A341435 nonn,base
%O A341435 1,2
%A A341435 _Amiram Eldar_, Feb 11 2021