A325868 - OEIS

%I #16 Oct 17 2020 02:33:30

%S 1,2,4,6,14,24,52,84,120,240,548,688,1784,2600,4236,5796,16200,17568,

%T 49968,55648,101360,176792,433736,430032,728784,1360928,2304840,

%U 2990856,8682912,7877376,25243200,27946656,46758912,81457248,121546416,114388320,442583952

%N Number of subsets of {1..n} containing n such that every ordered pair of distinct elements has a different quotient.

%H Fausto A. C. Cariboni, <a href="/A325868/b325868.txt">Table of n, a(n) for n = 1..50</a>

%e The a(1) = 1 through a(5) = 14 subsets:

%e   {1}  {2}    {3}      {4}      {5}

%e        {1,2}  {1,3}    {1,4}    {1,5}

%e               {2,3}    {2,4}    {2,5}

%e               {1,2,3}  {3,4}    {3,5}

%e                        {1,3,4}  {4,5}

%e                        {2,3,4}  {1,2,5}

%e                                 {1,3,5}

%e                                 {1,4,5}

%e                                 {2,3,5}

%e                                 {2,4,5}

%e                                 {3,4,5}

%e                                 {1,2,3,5}

%e                                 {1,3,4,5}

%e                                 {2,3,4,5}

%t Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&UnsameQ@@Divide@@@Subsets[#,{2}]&]],{n,10}]

%Y Cf. A025582, A108917, A143823, A196723, A196724.

%Y Cf. A325853, A325854, A325858, A325860, A325861, A325864, A325869.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jun 02 2019

%E a(21)-a(37) from _Fausto A. C. Cariboni_, Oct 16 2020