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A096826
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Number of maximal-sized antichains in divisor lattice D(n).
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3
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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
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1,2
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COMMENTS
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The divisor lattice D(n) is the lattice of the divisors of the natural number n.
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LINKS
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EXAMPLE
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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)
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PROG
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(Sage)
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 17 2004
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EXTENSIONS
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STATUS
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approved
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