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 A269987 Numbers n having factorial fractility A269982(n) = 5. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A269982 for a definition of factorial fractility and guide to related sequences. LINKS Robert Price, Table of n, a(n) for n = 1..70 EXAMPLE 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 that the factorial fractility of 68 is 5. MATHEMATICA 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]]; (* from Davin Park, Nov 19 2016 *) Select[Range[2, 500], A269982[#] == 5 &] (* Robert Price, Sep 19 2019 *) PROG (PARI) select( is_A269987(n)=A269982(n)==5, [1..400]) \\ M. F. Hasler, Nov 05 2018 CROSSREFS Cf. A000142 (factorial numbers), A269982 (factorial fractility of n); A269983, A269984, A269985, A269986, A269988 (numbers with factorial fractility 1, 2, ..., 6, respectively). Cf. A269570 (binary fractility), A270000 (harmonic fractility). Sequence in context: A043854 A043862 A043871 * A058906 A130694 A269748 Adjacent sequences:  A269984 A269985 A269986 * A269988 A269989 A269990 KEYWORD nonn AUTHOR Clark Kimberling and Peter J. C. Moses, Mar 11 2016 EXTENSIONS Edited and more terms added by M. F. Hasler, Nov 05 2018 STATUS approved

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Last modified June 14 12:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)