cp's OEIS Frontend

A269987 Numbers k having factorial fractility A269982(k) = 5.

%I A269987 #17 Oct 06 2023 03:27:41
%S A269987 68,70,71,85,92,100,126,127,130,136,138,145,154,157,161,164,168,180,
%T A269987 185,195,200,204,220,224,232,247,253,266,272,288,291,300,304,310,318,
%U A269987 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
%N A269987 Numbers k having factorial fractility A269982(k) = 5.
%C A269987 See A269982 for a definition of factorial fractility and a guide to related sequences.
%H A269987 Robert Price, <a href="/A269987/b269987.txt">Table of n, a(n) for n = 1..70</a>
%e A269987 NI(1/68) = (4, 2, 3, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, ...)
%e A269987 NI(4/68) = (3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, ...)
%e A269987 NI(6/68) = (3, 2, 1, 2, 2, 3, 1, 2, 3, 1, 1, 2, 1, 2, 2, 3, 1, 2, 3, ...)
%e A269987 NI(17/68) = (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...)
%e A269987 NI(34/68) = (2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...).
%e A269987 These 5 equivalence classes represent all the classes for n = 68, so the factorial fractility of 68 is 5.
%t A269987 A269982[n_] := CountDistinct[With[{l = NestWhileList[
%t A269987         Rescale[#, {1/(Floor[x] + 1)!, 1/Floor[x]!} /.
%t A269987            FindRoot[1/x! == #, {x, 1}]] &, #, UnsameQ, All]},
%t A269987      Min@l[[First@First@Position[l, Last@l] ;;]]] & /@
%t A269987    Range[1/n, 1 - 1/n, 1/n]]; (* _Davin Park_, Nov 19 2016 *)
%t A269987 Select[Range[2, 500], A269982[#] == 5 &] (* _Robert Price_, Sep 19 2019 *)
%o A269987 (PARI) select( is_A269987(n)=A269982(n)==5, [1..400]) \\ _M. F. Hasler_, Nov 05 2018
%Y A269987 Cf. A000142 (factorial numbers), A269982 (factorial fractility of n); A269983, A269984, A269985, A269986, A269988 (numbers with factorial fractility 1, 2, ..., 6, respectively).
%Y A269987 Cf. A269570 (binary fractility), A270000 (harmonic fractility).
%K A269987 nonn
%O A269987 1,1
%A A269987 _Clark Kimberling_ and _Peter J. C. Moses_, Mar 11 2016
%E A269987 Edited and more terms added by _M. F. Hasler_, Nov 05 2018