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A060209
Dunckley sequence: number of bases in which the n-th composite number is a Smith number.
2
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, 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, 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
OFFSET
1,8
REFERENCES
A. Vella and D. Vella, On Smith and Dunckley Numbers, Mathematics Today (Bull. Inst. Math. Appl), Vol. 37, No. 2 (2001), 54-56.
A. Vella and D. Vella, More Properties of Dunckley Numbers (in preparation).
LINKS
EXAMPLE
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.
A002808(5) = 10 is a Smith number in one base, 4, so a(5) = 1.
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]]; smithCount /@ Select[Range[100], CompositeQ] (* Amiram Eldar, Aug 21 2020 *)
CROSSREFS
Sequence in context: A238744 A030421 A085021 * A037830 A174353 A319582
KEYWORD
nonn,base
AUTHOR
Alfred and Dominic Vella (dunckley(AT)thevellas.freeserve.co.uk), Mar 19 2001
EXTENSIONS
a(1) added and offset corrected by Amiram Eldar, Aug 21 2020
STATUS
approved