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A096826 Number of maximal-sized antichains in divisor lattice D(n). 3
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 (list; graph; refs; listen; history; text; internal format)
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 A162915

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

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Last modified August 16 21:30 EDT 2022. Contains 356169 sequences. (Running on oeis4.)