cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A326492 Number of maximal subsets of {1..n} containing no quotients of pairs of distinct elements.

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%I A326492 #11 Sep 18 2019 04:05:36
%S A326492 1,1,2,2,3,3,4,4,4,5,7,7,10,10,16,18,31,31,47,47,52,62,104,104,130,
%T A326492 159,283,283,323,323,554,554,616,690,1248,1366,1871,1871,3567,3759,
%U A326492 5245,5245,8678,8678,9808,12148,23352,23352,27470,31695,45719,47187,54595,54595,95383,108199
%N A326492 Number of maximal subsets of {1..n} containing no quotients of pairs of distinct elements.
%F A326492 a(n) = A326496(n) + 1 for n > 1. - _Andrew Howroyd_, Aug 30 2019
%e A326492 The a(0) = 1 through a(9) = 5 subsets:
%e A326492   {}  {1}  {1}  {1}   {1}   {1}    {1}     {1}      {1}       {1}
%e A326492            {2}  {23}  {23}  {235}  {235}   {2357}   {23578}   {23578}
%e A326492                       {34}  {345}  {256}   {2567}   {25678}   {256789}
%e A326492                                    {3456}  {34567}  {345678}  {345678}
%e A326492                                                               {456789}
%t A326492 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A326492 Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Divide@@@Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&]]=={}&]]],{n,0,10}]
%Y A326492 Subsets with quotients are A326023.
%Y A326492 Subsets with quotients > 1 are A326079.
%Y A326492 Subsets without quotients are A327591.
%Y A326492 Maximal subsets without differences or quotients are A326491.
%Y A326492 Maximal subsets without quotients (or products) are A326496.
%Y A326492 Cf. A007865, A121269, A325860, A325994, A326117, A326489, A326490.
%K A326492 nonn
%O A326492 0,3
%A A326492 _Gus Wiseman_, Jul 09 2019
%E A326492 Terms a(16) and beyond from _Andrew Howroyd_, Aug 30 2019