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%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
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