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A068509
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a(n) = maximum length of a subset in {1,..,n} whose integers have pairwise l.c.m. not exceeding n.
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0
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1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Can be formulated as a maximum independent set problem and solved using integer linear programming: maximize sum {i = 1 to n} x[i] subject to x[i] + x[j] <= 1 for all i < j with lcm(i,j) > n, x[i] in {0,1} for all i. [From Rob Pratt (Rob.Pratt(AT)sas.com), Feb 08 2010]
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, B26.
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FORMULA
| (3*sqrt(n))/(2*sqrt(2)) - 2 < a(n) <= 1.638*sqrt(n) - P. Erdos and S. L. G. Choi
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CROSSREFS
| Sequence in context: A061071 A122258 * A070319 A057142 A098388 A157792
Adjacent sequences: A068506 A068507 A068508 * A068510 A068511 A068512
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KEYWORD
| easy,nonn
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AUTHOR
| Naohiro Nomoto (n_nomoto(AT)yabumi.com), Mar 12 2002
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EXTENSIONS
| More terms from Rob Pratt (Rob.Pratt(AT)sas.com), Feb 08 2010
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