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%I #7 Aug 21 2020 20:18:03
%S 0,0,0,0,1,0,1,2,1,1,1,1,1,1,2,1,3,1,2,2,1,3,1,2,1,1,1,4,1,2,3,1,2,2,
%T 2,3,1,4,1,3,3,5,1,4,3,1,3,1,1,5,6,2,2,1,1,7,1,2,2,4,6,1,2,1,2,1,2,1,
%U 4,1,1,2,2,2,5,3,7,3,2,4,1,1,6,3,1,4,2,3,2,3,1,1,1,5,2,4,1,5,5,1,3,2,1,5,3,2
%N Dunckley sequence: number of bases in which the n-th composite number is a Smith number.
%D A. Vella and D. Vella, On Smith and Dunckley Numbers, Mathematics Today (Bull. Inst. Math. Appl), Vol. 37, No. 2 (2001), 54-56.
%D A. Vella and D. Vella, More Properties of Dunckley Numbers (in preparation).
%H Amiram Eldar, <a href="/A060209/b060209.txt">Table of n, a(n) for n = 1..10000</a>
%e The first 4 composite numbers, 4, 6, 8, and 9, are not Smith numbers in any base, so a(n) = 0 for n = 1 to 4.
%e A002808(5) = 10 is a Smith number in one base, 4, so a(5) = 1.
%t 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]]; smithCount /@ Select[Range[100], CompositeQ] (* _Amiram Eldar_, Aug 21 2020 *)
%Y Cf. A002808, A006753.
%K nonn,base
%O 1,8
%A Alfred and Dominic Vella (dunckley(AT)thevellas.freeserve.co.uk), Mar 19 2001
%E a(1) added and offset corrected by _Amiram Eldar_, Aug 21 2020
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