A325860 - OEIS

%I #21 Oct 06 2020 02:20:55

%S 1,2,4,8,14,28,52,104,188,308,548,1096,1784,3568,6168,10404,16200,

%T 32400,49968,99936,155584,256944,433736,867472,1297504,2026288,

%U 3387216,5692056,8682912,17365824,25243200,50486400,78433056,125191968,206649216,328195632

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

%C Also subsets of {1..n} such that every orderless pair of (not necessarily distinct) elements has a different product.

%H Fausto A. C. Cariboni, <a href="/A325860/b325860.txt">Table of n, a(n) for n = 0..50</a>

%e The a(0) = 1 through a(4) = 14 subsets:

%e   {}  {}   {}    {}     {}

%e       {1}  {1}   {1}    {1}

%e            {2}   {2}    {2}

%e            {12}  {3}    {3}

%e                  {12}   {4}

%e                  {13}   {12}

%e                  {23}   {13}

%e                  {123}  {14}

%e                         {23}

%e                         {24}

%e                         {34}

%e                         {123}

%e                         {134}

%e                         {234}

%t Table[Length[Select[Subsets[Range[n]],UnsameQ@@Divide@@@Subsets[#,{2}]&]],{n,0,20}]

%Y The subset case is A325860.

%Y The maximal case is A325861.

%Y The integer partition case is A325853.

%Y The strict integer partition case is A325854.

%Y Heinz numbers of the counterexamples are given by A325994.

%Y Cf. A002033, A108917, A143823, A196723, A196723, A196724, A325855, A325858, A325859, A325868, A325869.

%K nonn

%O 0,2

%A _Gus Wiseman_, May 31 2019

%E a(21)-a(25) from _Alois P. Heinz_, Jun 07 2019

%E a(26)-a(35) from _Fausto A. C. Cariboni_, Oct 04 2020