A059571 From Mertens's conjecture (1): floor(sqrt(n)) - |M(n)|, where M is Mertens's function A002321.

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

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

Paolo Xausa, Table of n, a(n) for n = 1..10000

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: A153764 A348422 A294509 * A027052 A322508 A194438

Adjacent sequences: A059568 A059569 A059570 * A059572 A059573 A059574

Keyword

sign

Author

N. J. A. Sloane, Feb 16 2001

Status

approved