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A320536
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a(n) is the least cardinal of a partition of {1..n} into simple paths of its divisorial graph.
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2
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1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 8, 9, 9, 9, 9, 10, 9, 10, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 11, 12, 12, 12, 12, 13, 12, 13, 13, 13, 13, 14, 14, 15, 15, 14, 14, 15, 14, 15, 15, 15, 15, 16, 16
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OFFSET
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1,5
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COMMENTS
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Saias proves that n/6 <= a(n) for all positive integers, and a(n) < n/4 for n large enough. [clarified by Paul Revenant, Jul 08 2019]
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LINKS
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FORMULA
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a(n) = floor((n+1)/2) - floor(n/3) for n <=35.
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EXAMPLE
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a(30) = 5 with (13, 26, 1, 11, 22, 2, 14, 28, 7, 21, 3, 27, 9, 18, 6, 12, 24, 8, 16, 4, 20, 10, 30, 15, 5, 25), (17), (19), (23) and (29).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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