|
|
A096827
|
|
Number of antichains in divisor lattice D(n).
|
|
23
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 17 2004
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|