%I #10 Aug 30 2019 21:47:16

%S 1,2,3,5,9,17,25,49,73,145,217,433,553,1105,1657,2593,3937,7873,10057,

%T 20113,26689,42321,63481,126961,154801,309601,464401,737569,992161,

%U 1984321,2450881,4901761,6292801,10197313,15295969,26241697,32947489,65894977,98842465,161587873,205842529

%N Number of subsets of {1..n} containing all of their integer quotients.

%C These are sets that are closed under taking the quotient of two (not necessarily distinct) divisible terms.

%F For n > 0, a(n) = A326078(n) + 1.

%e The a(0) = 1 through a(5) = 17 subsets:

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

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

%e {1,2} {1,2} {1,2} {1,2}

%e {1,3} {1,3} {1,3}

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

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

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

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

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

%e {1,3,4}

%e {1,3,5}

%e {1,4,5}

%e {1,2,3,4}

%e {1,2,3,5}

%e {1,2,4,5}

%e {1,3,4,5}

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

%t Table[Length[Select[Subsets[Range[n]],SubsetQ[#,Select[Divide@@@Tuples[#,2],IntegerQ]]&]],{n,0,10}]

%Y Cf. A007865, A051026, A054519, A067992, A103580, A325853, A325854, A325860, A325861, A325994, A326078.

%K nonn

%O 0,2

%A _Gus Wiseman_, Jun 04 2019

%E Terms a(21) and beyond from _Andrew Howroyd_, Aug 30 2019