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A269988 Numbers k having factorial fractility A269982(k) = 6.

%I A269988 #19 Oct 05 2023 08:34:50
%S A269988 94,105,115,141,142,153,170,175,182,184,187,189,196,205,207,210,212,
%T A269988 213,215,221,225,235,245,252,254,255,260,265,275,276,282,290,299,306,
%U A269988 314,325,367,368,370,378,381,388,392,399,414,424,425,426,434,435,446,450
%N A269988 Numbers k having factorial fractility A269982(k) = 6.
%C A269988 See A269982 for a definition of factorial fractility and a guide to related sequences.
%H A269988 Robert Price, <a href="/A269988/b269988.txt">Table of n, a(n) for n = 1..60</a>
%e A269988 NI(1/94) = (4, 3, 2, 3, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, 3, 1, 4, 1, 1, 2, ...),
%e A269988 NI(2/94) = (4, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, ...),
%e A269988 NI(4/94) = (3, 5, 1, 1, 2, 2, 1, 3, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, ...),
%e A269988 NI(7/94) = (3, 2, 2, 2, 1, 2, 4, 3, 2, 3, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, ...),
%e A269988 NI(11/94) = (3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, ...),
%e A269988 NI(47/94) = (2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...):
%e A269988 These 6 equivalence classes represent all the classes for k = 94, so the factorial fractility of 94 is 6.
%t A269988 A269982[n_] := CountDistinct[With[{l = NestWhileList[
%t A269988          Rescale[#, {1/(Floor[x] + 1)!, 1/Floor[x]!} /.
%t A269988             FindRoot[1/x! == #, {x, 1}]] &, #, UnsameQ, All]},
%t A269988       Min@l[[First@First@Position[l, Last@l] ;;]]] & /@
%t A269988     Range[1/n, 1 - 1/n, 1/n]]; (* _Davin Park_, Nov 19 2016 *)
%t A269988 Select[Range[2, 500], A269982[#] == 6 &] (* _Robert Price_, Sep 19 2019 *)
%o A269988 (PARI) select( is_A269988(n)=A269982(n)==6, [1..400]) \\ _M. F. Hasler_, Nov 05 2018
%Y A269988 Cf. A000142 (factorial numbers), A269982 (factorial fractility of n); A269983, A269984, A269985, A269986, A269987 (numbers with factorial fractility 1, 2, ..., 5, respectively).
%Y A269988 Cf. A269570 (binary fractility), A270000 (harmonic fractility).
%K A269988 nonn
%O A269988 1,1
%A A269988 _Clark Kimberling_ and _Peter J. C. Moses_, Mar 11 2016
%E A269988 Edited and more terms added by _M. F. Hasler_, Nov 05 2018