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 A337294 #9 Nov 07 2024 15:20:29
%S A337294 4,10,15,27,42,60,72,78,174,204,222,378,438,663,1352,1446,2022,2526,
%T A337294 2598,3462,4038,4542,6054,12102,22182,30336,35432,39318,44358,55446,
%U A337294 72582,90726,99798,110886,120966,157254,181446,235878,288294,332646,399174,432438,665286
%N A337294 Composite numbers k that are Smith numbers in a record number of bases 1 < b <= k.
%C A337294 Values of A002808 at the indices of records of A060209.
%C A337294 The corresponding number of bases are 0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 15, 19, 20, 21, 22, 27, 29, 31, 33, 35, 40, 48, 59, 66, 67, 71, 76, 80, 81, 88, 97, 98, 101, 105, 118, 119, 130, 131, 152, 156, 167, 187, ...
%e A337294 a(1) = 4 since it is the least composite number and it is not a Smith number in any base 1 < b <= 4.
%e A337294 a(2) = 10 since it is the least number that is a Smith number in any base 1 < b <= 10: 10 = 2 * 5 is, 22_4 = 2_4 * 11_4 in base 4, and 2 + 2 = 2 + (1 + 1) = 4.
%t A337294 digSum[n_, b_] := Plus @@ IntegerDigits[n, b]; smithCount[n_] := If[! CompositeQ[n], 0, Module[{c = 0, f = FactorInteger[n]}, p = f[[;; , 1]]; e = f[[;; , 2]]; Do[If[Total[e*(digSum[#, b] & /@ p)] == digSum[n, b], c++], {b, 2, n}]; c]]; seq = {}; cmax = -1; Do[If[CompositeQ[n] && (c = smithCount[n]) > cmax, cmax = c; AppendTo[seq, n]], {n, 1, 666}]; seq
%Y A337294 Cf. A002808, A006753, A060209.
%Y A337294 Similar sequences: A107129, A330813.
%K A337294 nonn,base
%O A337294 1,1
%A A337294 _Amiram Eldar_, Aug 21 2020