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A326077 Number of maximal primitive subsets of {1..n}.

%I A326077 #20 Sep 07 2020 03:35:42
%S A326077 1,1,2,2,3,3,4,4,6,7,11,11,13,13,23,24,36,36,48,48,64,66,126,126,150,
%T A326077 151,295,363,507,507,595,595,895,903,1787,1788,2076,2076,4132,4148,
%U A326077 5396,5396,6644,6644,9740,11172,22300,22300,26140,26141,40733,40773,60333,60333,80781,80783
%N A326077 Number of maximal primitive subsets of {1..n}.
%C A326077 a(n) is the number of maximal primitive subsets of {1, ..., n}.  Here primitive means that no element of the subset divides any other and maximal means that no element can be added to the subset while maintaining the property of being pairwise indivisible. - _Nathan McNew_, Aug 10 2020
%H A326077 Nathan McNew, <a href="/A326077/b326077.txt">Table of n, a(n) for n = 0..300</a>
%e A326077 The a(0) = 1 through a(9) = 7 sets:
%e A326077   {}  {1}  {1}  {1}   {1}   {1}    {1}    {1}     {1}     {1}
%e A326077            {2}  {23}  {23}  {235}  {235}  {2357}  {2357}  {2357}
%e A326077                       {34}  {345}  {345}  {3457}  {3457}  {2579}
%e A326077                                    {456}  {4567}  {3578}  {3457}
%e A326077                                                   {4567}  {3578}
%e A326077                                                   {5678}  {45679}
%e A326077                                                           {56789}
%t A326077 stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
%t A326077 fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
%t A326077 Table[Length[fasmax[Select[Subsets[Range[n]],stableQ[#,Divisible]&]]],{n,0,10}]
%o A326077 (PARI)
%o A326077 divset(n)={sumdiv(n, d, if(d<n, 1 << d))}
%o A326077 a(n)={my(p=vector(n, k, divset(k)), d=0); for(i=1, #p, d=bitor(d, p[i]));
%o A326077 my(ismax(b)=my(e=0); forstep(k=#p, 1, -1, if(bittest(b, k), e=bitor(e, p[k]), if(!bittest(e, k) && !bitand(p[k], b), return(0)) )); 1);
%o A326077 ((k, b)->if(k>#p, ismax(b), my(f=!bitand(p[k], b)); if(!f || bittest(d, k), self()(k+1, b)) + if(f, self()(k+1, b+(1<<k)))))(1, 0)} \\ _Andrew Howroyd_, Aug 30 2019
%Y A326077 Cf. A001055, A051026 (all primitive subsets), A067992, A096827, A143824, A285572, A285573, A303362, A305148, A305149, A316476, A325861, A326023, A326082.
%K A326077 nonn
%O A326077 0,3
%A A326077 _Gus Wiseman_, Jun 05 2019
%E A326077 Terms a(19) to a(55) from _Andrew Howroyd_, Aug 30 2019
%E A326077 Name edited by _Nathan McNew_, Aug 10 2020