cp's OEIS Frontend

A096827 Number of antichains in divisor lattice D(n).

%I A096827 #19 Aug 26 2018 13:21:46
%S A096827 2,3,3,4,3,6,3,5,4,6,3,10,3,6,6,6,3,10,3,10,6,6,3,15,4,6,5,10,3,20,3,
%T A096827 7,6,6,6,20,3,6,6,15,3,20,3,10,10,6,3,21,4,10,6,10,3,15,6,15,6,6,3,50,
%U A096827 3,6,10,8,6,20,3,10,6,20,3,35,3,6,10,10,6,20,3,21,6,6,3,50,6,6,6,15,3,50,6
%N A096827 Number of antichains in divisor lattice D(n).
%C A096827 The divisor lattice D(n) is the lattice of the divisors of the natural number n.
%C A096827 The empty set is counted as an antichain in D(n).
%C A096827 a(n) = gamma(n+1) where gamma is degree of cardinal completeness of Łukasiewicz n-valued logic. - _Artur Jasinski_, Mar 01 2010
%D A096827 Alexander S. Karpenko, Lukasiewicz's Logics and Prime Numbers, Luniver Press, Beckington, 2006. See Table I p. 113.
%H A096827 Arkadiusz Wesolowski, <a href="/A096827/b096827.txt">Table of n, a(n) for n = 1..990</a>
%H A096827 <a href="/index/Lu#Lukasiewicz">Index entries for sequences related to Łukasiewicz</a>
%F A096827 a(n) = A285573(n) + 1. - _Gus Wiseman_, Aug 24 2018
%t A096827 nn=200;
%t A096827 stableSets[u_,Q_]:=If[Length[u]===0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r===w||Q[r,w]||Q[w,r]],Q]]]];
%t A096827 Table[Length[stableSets[Divisors[n],Divisible]],{n,nn}] (* _Gus Wiseman_, Aug 24 2018 *)
%Y A096827 Cf. A096825, A096826, A097699.
%Y A096827 Cf. A175177, A175178. - _Artur Jasinski_, Mar 01 2010
%Y A096827 Cf. A000005, A008480, A253249, A285572 A285573.
%K A096827 nonn
%O A096827 1,1
%A A096827 Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 17 2004
%E A096827 More terms from _John W. Layman_, Aug 20 2004