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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

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.

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 September 19 08:43 EDT 2019. Contains 327189 sequences. (Running on oeis4.)