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 A059571 From Mertens's conjecture (1): floor(sqrt(n)) - |M(n)|, where M is Mertens's function A002321. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS 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. REFERENCES 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. LINKS A. M. Odlyzko and H. J. J. te Riele, Disproof of the Mertens conjecture, J. reine angew. Math., 357 (1985), pp. 138-160. MATHEMATICA Table[Floor[Sqrt[n]] - Abs[Plus @@ MoebiusMu[Range[n]]], {n, 1, 80}] (* Carl Najafi, Aug 17 2011 *) CROSSREFS Cf. A002321, A059572, A059581. Sequence in context: A229899 A153764 A294509 * A027052 A322508 A194438 Adjacent sequences:  A059568 A059569 A059570 * A059572 A059573 A059574 KEYWORD sign AUTHOR N. J. A. Sloane, Feb 16 2001 STATUS approved

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Last modified April 17 06:46 EDT 2021. Contains 343059 sequences. (Running on oeis4.)