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A325860 Number of subsets of {1..n} such that every pair of distinct elements has a different quotient.

%I A325860 #21 Oct 06 2020 02:20:55
%S A325860 1,2,4,8,14,28,52,104,188,308,548,1096,1784,3568,6168,10404,16200,
%T A325860 32400,49968,99936,155584,256944,433736,867472,1297504,2026288,
%U A325860 3387216,5692056,8682912,17365824,25243200,50486400,78433056,125191968,206649216,328195632
%N A325860 Number of subsets of {1..n} such that every pair of distinct elements has a different quotient.
%C A325860 Also subsets of {1..n} such that every orderless pair of (not necessarily distinct) elements has a different product.
%H A325860 Fausto A. C. Cariboni, <a href="/A325860/b325860.txt">Table of n, a(n) for n = 0..50</a>
%e A325860 The a(0) = 1 through a(4) = 14 subsets:
%e A325860   {}  {}   {}    {}     {}
%e A325860       {1}  {1}   {1}    {1}
%e A325860            {2}   {2}    {2}
%e A325860            {12}  {3}    {3}
%e A325860                  {12}   {4}
%e A325860                  {13}   {12}
%e A325860                  {23}   {13}
%e A325860                  {123}  {14}
%e A325860                         {23}
%e A325860                         {24}
%e A325860                         {34}
%e A325860                         {123}
%e A325860                         {134}
%e A325860                         {234}
%t A325860 Table[Length[Select[Subsets[Range[n]],UnsameQ@@Divide@@@Subsets[#,{2}]&]],{n,0,20}]
%Y A325860 The subset case is A325860.
%Y A325860 The maximal case is A325861.
%Y A325860 The integer partition case is A325853.
%Y A325860 The strict integer partition case is A325854.
%Y A325860 Heinz numbers of the counterexamples are given by A325994.
%Y A325860 Cf. A002033, A108917, A143823, A196723, A196723, A196724, A325855, A325858, A325859, A325868, A325869.
%K A325860 nonn
%O A325860 0,2
%A A325860 _Gus Wiseman_, May 31 2019
%E A325860 a(21)-a(25) from _Alois P. Heinz_, Jun 07 2019
%E A325860 a(26)-a(35) from _Fausto A. C. Cariboni_, Oct 04 2020