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Search: id:A096825
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| A096825 |
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Maximal size of an antichain in divisor lattice D(n). |
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3
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| 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 4, 1, 2, 2, 1, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 1, 4, 2, 2, 2, 2, 1, 4, 2, 2, 2, 2, 2, 2, 1, 2, 2, 3
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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The divisor lattice D(n) is the lattice of the divisors of the natural number n.
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FORMULA
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a(n) is the coefficient at x^k in (1+x+...+x^k_1)*...*(1+x+...+x^k_q) where n=p_1^k_1*...*p_q^k_q is the prime factorization of n and k=floor((k_1+...+k_q)/2). - Alec Mihailovs (alec(AT)mihailovs.com), Aug 22 2004
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MAPLE
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a:=proc(n) local klist, x; klist:=ifactors(n)[2, 1..-1, 2]; coeff(normal(mul((1-x^(k+1))/(1-x), k=klist)), x, floor(add(k, k=klist)/2)) end: seq(a(n), n=1..100);
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CROSSREFS
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Cf. A096826, A096827.
Sequence in context: A079553 A001221 A064372 this_sequence A007875 A050320 A121382
Adjacent sequences: A096822 A096823 A096824 this_sequence A096826 A096827 A096828
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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) and Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 17 2004
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EXTENSIONS
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More terms from Alec Mihailovs (alec(AT)mihailovs.com), Aug 22 2004
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