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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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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Mertens conjectured that |A002321(n)| < sqrt(n) for all n>1. This is now known to be false.
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REFERENCES
| D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VI.2.
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LINKS
| 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
| Table[Floor[Sqrt[n]] - Plus @@ MoebiusMu[Range[n]], {n, 1, 80}] (* Carl Najafi, Aug 17 2011 *)
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CROSSREFS
| Cf. A059571, A002321.
Sequence in context: A067349 A108414 A097477 * A031249 A031232 A030583
Adjacent sequences: A059569 A059570 A059571 * A059573 A059574 A059575
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 16 2001
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