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A059572
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From Mertens's conjecture (2): floor(sqrt(n)) - Mertens's function A002321(n).
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2
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0, 1, 2, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 5, 4, 5, 6, 6, 7, 7, 6, 5, 6, 6, 7, 6, 6, 6, 7, 8, 9, 9, 8, 7, 6, 7, 8, 7, 6, 6, 7, 8, 9, 9, 9, 8, 9, 9, 10, 10, 9, 9, 10, 10, 9, 9, 8, 7, 8, 8, 9, 8, 8, 9, 8, 9, 10, 10, 9, 10, 11, 11, 12, 11, 11, 11, 10, 11, 12, 12, 13, 12, 13
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OFFSET
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1,3
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COMMENTS
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Mertens conjectured that |A002321(n)| < sqrt(n) for all n > 1. This is now known to be false.
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REFERENCES
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D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VI.2.
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LINKS
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MATHEMATICA
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Table[Floor[Sqrt[n]] - Plus @@ MoebiusMu[Range[n]], {n, 1, 80}] (* Carl Najafi, Aug 17 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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