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A059571
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From Mertens' conjecture (1): Floor(sqrt(n)) - |M(n)|, where M is Mertens' function A002321.
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4
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0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 1, 2, 3, 2, 2, 1, 1, 2, 3, 2, 2, 3, 4, 4, 4, 3, 2, 1, 1, 2, 3, 4, 5, 4, 5, 6, 6, 5, 4, 3, 3, 3, 4, 3, 3, 4, 4, 5, 5, 4, 4, 5, 5, 6, 7, 6, 6, 5, 6, 6, 7, 8, 7, 6, 6, 7, 6, 5, 5, 4, 5, 5, 5, 6, 5, 4, 4, 5, 6, 5, 5, 6, 7, 8, 8, 7, 7, 8, 8, 9
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OFFSET
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1,10
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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. So eventually there will be negative terms.
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REFERENCES
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D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VI.2.
K. H. Rosen et al., eds., Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000; p. 267.
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LINKS
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Table of n, a(n) for n=1..93.
A. M. Odlyzko and H. J. J. te Riele, Disproof of the Mertens conjecture, J. reine angew. Math., 357 (1985), pp. 138-160.
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MATHEMATICA
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Table[Floor[Sqrt[n]] - Abs[Plus @@ MoebiusMu[Range[n]]], {n, 1, 80}] (* Carl Najafi, Aug 17 2011 *)
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CROSSREFS
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Cf. A059572, A002321, A059581.
Sequence in context: A131334 A004602 A153764 * A027052 A194438 A144409
Adjacent sequences: A059568 A059569 A059570 * A059572 A059573 A059574
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane, Feb 16 2001
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STATUS
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approved
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