cp's OEIS Frontend

A326490 Number of subsets of {1..n} containing no differences or quotients of pairs of distinct elements.

%I A326490 #21 Oct 24 2020 02:30:54
%S A326490 1,2,3,5,7,12,18,31,46,72,102,172,259,428,607,989,1329,2142,3117,4953,
%T A326490 6956,11032,15321,23979,33380,48699,66849,104853,144712,220758,304133,
%U A326490 461580,636556,973843,1316513,1958828,2585433,3882843,5237093,7884277,10555739,15729293
%N A326490 Number of subsets of {1..n} containing no differences or quotients of pairs of distinct elements.
%H A326490 Fausto A. C. Cariboni, <a href="/A326490/b326490.txt">Table of n, a(n) for n = 0..90</a>
%F A326490 For n > 0, a(n) = A326495(n) + 1.
%e A326490 The a(0) = 1 through a(6) = 18 subsets:
%e A326490   {}  {}   {}   {}     {}     {}       {}
%e A326490       {1}  {1}  {1}    {1}    {1}      {1}
%e A326490            {2}  {2}    {2}    {2}      {2}
%e A326490                 {3}    {3}    {3}      {3}
%e A326490                 {2,3}  {4}    {4}      {4}
%e A326490                        {2,3}  {5}      {5}
%e A326490                        {3,4}  {2,3}    {6}
%e A326490                               {2,5}    {2,3}
%e A326490                               {3,4}    {2,5}
%e A326490                               {3,5}    {2,6}
%e A326490                               {4,5}    {3,4}
%e A326490                               {3,4,5}  {3,5}
%e A326490                                        {4,5}
%e A326490                                        {4,6}
%e A326490                                        {5,6}
%e A326490                                        {2,5,6}
%e A326490                                        {3,4,5}
%e A326490                                        {4,5,6}
%t A326490 Table[Length[Select[Subsets[Range[n]],Intersection[#,Union[Divide@@@Reverse/@Subsets[#,{2}],Subtract@@@Reverse/@Subsets[#,{2}]]]=={}&]],{n,0,10}]
%o A326490 (PARI)
%o A326490 a(n)={
%o A326490    my(recurse(k, b)=
%o A326490     if(k > n, 1,
%o A326490       my(t = self()(k + 1, b));
%o A326490       for(i=1, k\2, if(bittest(b,i) && (bittest(b,k-i) || (!(k%i) && bittest(b,k/i))), return(t)));
%o A326490       t += self()(k + 1, b + (1<<k));
%o A326490       t);
%o A326490    );
%o A326490    if(n, recurse(2, 0)) + 1;
%o A326490 } \\ _Andrew Howroyd_, Aug 25 2019
%Y A326490 Subsets without difference are A007865.
%Y A326490 Maximal subsets without differences or quotients are A326491.
%Y A326490 Subsets without quotients are A327591.
%Y A326490 Subsets with differences and quotients are A326494.
%Y A326490 Cf. A051026, A054519, A325860, A326023, A326079, A326489.
%K A326490 nonn
%O A326490 0,2
%A A326490 _Gus Wiseman_, Jul 09 2019
%E A326490 a(19)-a(41) from _Andrew Howroyd_, Aug 25 2019