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A269986
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Numbers k having factorial fractility A269982(k) = 4.
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7
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20, 28, 34, 35, 40, 45, 46, 47, 50, 51, 56, 60, 63, 65, 69, 75, 77, 80, 82, 84, 90, 91, 102, 110, 112, 116, 117, 120, 123, 124, 133, 135, 144, 147, 148, 150, 152, 156, 159, 160, 165, 167, 171, 172, 194, 206, 208, 209, 216, 217, 222, 223, 234, 236, 239, 240
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OFFSET
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1,1
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COMMENTS
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See A269982 for a definition of factorial fractility and a guide to related sequences.
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LINKS
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EXAMPLE
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NI(1/20) = (3, 3, 2, 3, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 3, 2, ...)
NI(5/20) = (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...)
NI(6/20) = (2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...)
NI(10/20) = (2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...).
These 4 equivalence classes represent all the classes for n = 20, so the factorial fractility of 20 is 4.
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MATHEMATICA
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A269982[n_] := CountDistinct[With[{l = NestWhileList[
Rescale[#, {1/(Floor[x] + 1)!, 1/Floor[x]!} /.
FindRoot[1/x! == #, {x, 1}]] &, #, UnsameQ, All]},
Min@l[[First@First@Position[l, Last@l] ;; ]]] & /@
Range[1/n, 1 - 1/n, 1/n]]; (* Davin Park, Nov 19 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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