A096826 - OEIS

A096826

Number of maximal-sized antichains in divisor lattice D(n).

1, 2, 2, 3, 2, 1, 2, 4, 3, 1, 2, 3, 2, 1, 1, 5, 2, 3, 2, 3, 1, 1, 2, 6, 3, 1, 4, 3, 2, 2, 2, 6, 1, 1, 1, 1, 2, 1, 1, 6, 2, 2, 2, 3, 3, 1, 2, 10, 3, 3, 1, 3, 2, 6, 1, 6, 1, 1, 2, 1, 2, 1, 3, 7, 1, 2, 2, 3, 1, 2, 2, 4, 2, 1, 3, 3, 1, 2, 2, 10, 5, 1, 2, 1, 1, 1

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OFFSET

1,2

COMMENTS

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

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..10000

EXAMPLE

From Gus Wiseman, Aug 24 2018: (Start)

The a(120) = 6 antichains:

{8,12,20,30}

{8,12,15,20}

{8,10,12,15}

{6,8,15,20}

{6,8,10,15}

{4,6,10,15}

(End)

PROG

(Sage)

def A096826(n) :

if n==1 : return 1

R.<t> = QQ[]; mults = [x[1] for x in factor(n)]

maxsize = prod((t^(m+1)-1)//(t-1) for m in mults)[sum(mults)//2]

dlat = LatticePoset((divisors(n), attrcall("divides")))

count = 0

for ac in dlat.antichains_iterator() :

if len(ac) == maxsize : count += 1

return count

# Eric M. Schmidt, May 13 2013

CROSSREFS

Cf. A000005, A008480, A096825, A096827, A253249, A285572 A285573.

Sequence in context: A030362 A007906 A044050 * A346010 A116199 A369031

Adjacent sequences: A096823 A096824 A096825 * A096827 A096828 A096829

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms from Eric M. Schmidt, May 13 2013

STATUS

approved