%I #20 Sep 07 2020 03:35:42

%S 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 151,295,363,507,507,595,595,895,903,1787,1788,2076,2076,4132,4148,

%U 5396,5396,6644,6644,9740,11172,22300,22300,26140,26141,40733,40773,60333,60333,80781,80783

%N Number of maximal primitive subsets of {1..n}.

%C 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 Nathan McNew, <a href="/A326077/b326077.txt">Table of n, a(n) for n = 0..300</a>

%e The a(0) = 1 through a(9) = 7 sets:

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

%e {2} {23} {23} {235} {235} {2357} {2357} {2357}

%e {34} {345} {345} {3457} {3457} {2579}

%e {456} {4567} {3578} {3457}

%e {4567} {3578}

%e {5678} {45679}

%e {56789}

%t stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];

%t fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];

%t Table[Length[fasmax[Select[Subsets[Range[n]],stableQ[#,Divisible]&]]],{n,0,10}]

%o (PARI)

%o divset(n)={sumdiv(n, d, if(d<n, 1 << d))}

%o a(n)={my(p=vector(n, k, divset(k)), d=0); for(i=1, #p, d=bitor(d, p[i]));

%o 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 ((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 Cf. A001055, A051026 (all primitive subsets), A067992, A096827, A143824, A285572, A285573, A303362, A305148, A305149, A316476, A325861, A326023, A326082.

%K nonn

%O 0,3

%A _Gus Wiseman_, Jun 05 2019

%E Terms a(19) to a(55) from _Andrew Howroyd_, Aug 30 2019

%E Name edited by _Nathan McNew_, Aug 10 2020