A175177 -id:A175177 - cp's OEIS frontend

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

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

nonn

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

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

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..990
Index entries for sequences related to Łukasiewicz

Cf. A096825, A096826, A097699.
Cf. A175177, A175178. - Artur Jasinski, Mar 01 2010
Cf. A000005, A008480, A253249, A285572 A285573.

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 *)

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

More terms from John W. Layman, Aug 20 2004

A175178 a(n)=Values of cardinality of rooted trees CRT for successive primes.

Original entry on oeis.org

1, 1, 1, 2, 1, 5, 1, 1, 1, 1, 1, 2, 4, 6, 1, 1, 2, 9, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 5, 6, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 16, 1, 9, 2, 1, 1, 1, 1, 1, 7, 1, 19, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 6, 3, 1, 1, 2, 1, 11, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1

Offset: 1

Artur Jasinski, Mar 01 2010

nonn

Karpenko A.S. 2006. Lukasiewicz's Logics and Prime Numbers (English translation).
Karpenko A.S. 2000. Lukasiewicz's Logics and Prime Numbers (Russian).

A058340, A058340, A096827, A175177.

A175179 Primes for which value of CRT (Cardinality of rooted tree) is equal to 1.

Original entry on oeis.org

2, 3, 5, 11, 17, 19, 23, 29, 31, 47, 53, 67, 71, 79, 83, 89, 97, 101, 103, 107, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 191, 199

Offset: 1

Artur Jasinski, Mar 01 2010

nonn

Primes p = Prime(x) such that A175178(x)=1.

Karpenko A.S. 2006. Lukasiewicz's Logics and Prime Numbers (English translation).
Karpenko A.S. 2000. Lukasiewicz's Logics and Prime Numbers (Russian).

Cf. A096827, A175177, A175178.

A173883 a(n) = number of iterations in the sequence of classes of prime numbers for prime(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 6, 5, 4, 4, 4, 4, 4, 6, 4, 5, 4, 5, 4, 5, 5, 4, 4, 4, 4, 5, 6, 5, 4, 6, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8

Offset: 2

Artur Jasinski, Mar 01 2010

nonn

Alexander S. Karpenko, Lukasiewicz's Logics and Prime Numbers, Luniver Press, Beckington, 2006, pp. 98-102.

Cf. A058340, A096827, A175177, A175178, A175179.

Edited, corrected and extended by Arkadiusz Wesolowski, Jan 19 2013

cp's OEIS Frontend

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

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A175178 a(n)=Values of cardinality of rooted trees CRT for successive primes.

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A175179 Primes for which value of CRT (Cardinality of rooted tree) is equal to 1.

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A173883 a(n) = number of iterations in the sequence of classes of prime numbers for prime(n).

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