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A269987
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Numbers k having factorial fractility A269982(k) = 5.
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7
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68, 70, 71, 85, 92, 100, 126, 127, 130, 136, 138, 145, 154, 157, 161, 164, 168, 180, 185, 195, 200, 204, 220, 224, 232, 247, 253, 266, 272, 288, 291, 300, 304, 310, 318, 324, 328, 333, 334, 336, 341, 342, 348, 360, 365, 369, 371, 390, 395, 400, 404, 407, 408, 412, 418, 433, 440, 441, 443, 444, 447
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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(1/68) = (4, 2, 3, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, ...)
NI(4/68) = (3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, ...)
NI(6/68) = (3, 2, 1, 2, 2, 3, 1, 2, 3, 1, 1, 2, 1, 2, 2, 3, 1, 2, 3, ...)
NI(17/68) = (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...)
NI(34/68) = (2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...).
These 5 equivalence classes represent all the classes for n = 68, so the factorial fractility of 68 is 5.
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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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