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

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, 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, 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

Offset

1,1

Comments

The divisor lattice D(n) is the lattice of the divisors of the natural number n.

The empty set is counted as an antichain in D(n).

a(n) = gamma(n+1) where gamma is degree of cardinal completeness of Łukasiewicz n-valued logic. - Artur Jasinski, Mar 01 2010

References

Alexander S. Karpenko, Lukasiewicz's Logics and Prime Numbers, Luniver Press, Beckington, 2006. See Table I p. 113.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..990

Index entries for sequences related to Łukasiewicz

Formula

a(n) = A285573(n) + 1. - Gus Wiseman, Aug 24 2018

Mathematica

nn=200;
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]]]];
Table[Length[stableSets[Divisors[n], Divisible]], {n, nn}] (* Gus Wiseman, Aug 24 2018 *)

Crossrefs

Cf. A096825, A096826, A097699.

Cf. A175177, A175178. - Artur Jasinski, Mar 01 2010

Cf. A000005, A008480, A253249, A285572 A285573.

Sequence in context: A186971 A329255 A262535 * A298321 A226142 A063826

Adjacent sequences: A096824 A096825 A096826 * A096828 A096829 A096830

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 17 2004

Extensions

More terms from John W. Layman, Aug 20 2004

Status

approved