A269988 - OEIS

%I #19 Oct 05 2023 08:34:50

%S 94,105,115,141,142,153,170,175,182,184,187,189,196,205,207,210,212,

%T 213,215,221,225,235,245,252,254,255,260,265,275,276,282,290,299,306,

%U 314,325,367,368,370,378,381,388,392,399,414,424,425,426,434,435,446,450

%N Numbers k having factorial fractility A269982(k) = 6.

%C See A269982 for a definition of factorial fractility and a guide to related sequences.

%H Robert Price, <a href="/A269988/b269988.txt">Table of n, a(n) for n = 1..60</a>

%e NI(1/94) = (4, 3, 2, 3, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, 3, 1, 4, 1, 1, 2, ...),

%e NI(2/94) = (4, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, ...),

%e NI(4/94) = (3, 5, 1, 1, 2, 2, 1, 3, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, ...),

%e NI(7/94) = (3, 2, 2, 2, 1, 2, 4, 3, 2, 3, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, ...),

%e NI(11/94) = (3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, ...),

%e NI(47/94) = (2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...):

%e These 6 equivalence classes represent all the classes for k = 94, so the factorial fractility of 94 is 6.

%t A269982[n_] := CountDistinct[With[{l = NestWhileList[

%t          Rescale[#, {1/(Floor[x] + 1)!, 1/Floor[x]!} /.

%t             FindRoot[1/x! == #, {x, 1}]] &, #, UnsameQ, All]},

%t       Min@l[[First@First@Position[l, Last@l] ;;]]] & /@

%t     Range[1/n, 1 - 1/n, 1/n]]; (* _Davin Park_, Nov 19 2016 *)

%t Select[Range[2, 500], A269982[#] == 6 &] (* _Robert Price_, Sep 19 2019 *)

%o (PARI) select( is_A269988(n)=A269982(n)==6, [1..400]) \\ _M. F. Hasler_, Nov 05 2018

%Y Cf. A000142 (factorial numbers), A269982 (factorial fractility of n); A269983, A269984, A269985, A269986, A269987 (numbers with factorial fractility 1, 2, ..., 5, respectively).

%Y Cf. A269570 (binary fractility), A270000 (harmonic fractility).

%K nonn

%O 1,1

%A _Clark Kimberling_ and _Peter J. C. Moses_, Mar 11 2016

%E Edited and more terms added by _M. F. Hasler_, Nov 05 2018