A337294 Composite numbers k that are Smith numbers in a record number of bases 1 < b <= k.
4, 10, 15, 27, 42, 60, 72, 78, 174, 204, 222, 378, 438, 663, 1352, 1446, 2022, 2526, 2598, 3462, 4038, 4542, 6054, 12102, 22182, 30336, 35432, 39318, 44358, 55446, 72582, 90726, 99798, 110886, 120966, 157254, 181446, 235878, 288294, 332646, 399174, 432438, 665286
Offset: 1
Examples
a(1) = 4 since it is the least composite number and it is not a Smith number in any base 1 < b <= 4. 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.
Programs
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Mathematica
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
Comments