

A059571


From Mertens' conjecture (1): Floor(sqrt(n))  M(n), where M is Mertens' 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
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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. 138160.


MATHEMATICA

Table[Floor[Sqrt[n]]  Abs[Plus @@ MoebiusMu[Range[n]]], {n, 1, 80}] (* Carl Najafi, Aug 17 2011 *)


CROSSREFS

Cf. A059572, A002321, A059581.
Sequence in context: A247418 A229899 A153764 * A027052 A194438 A144409
Adjacent sequences: A059568 A059569 A059570 * A059572 A059573 A059574


KEYWORD

sign


AUTHOR

N. J. A. Sloane, Feb 16 2001


STATUS

approved



