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

1,1

Comments

Values of A002808 at the indices of records of A060209.

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, ...

Links

Table of n, a(n) for n=1..43.

Example

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.

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

Crossrefs

Cf. A002808, A006753, A060209.

Similar sequences: A107129, A330813.

Sequence in context: A310472 A360557 A005662 * A259262 A218211 A302197

Adjacent sequences: A337291 A337292 A337293 * A337295 A337296 A337297

Keyword

nonn,base

Author

Amiram Eldar, Aug 21 2020

Status

approved