A059572 From Mertens's conjecture (2): floor(sqrt(n)) - Mertens's function A002321(n).

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

Offset

1,3

Comments

Mertens conjectured that |A002321(n)| < sqrt(n) for all n > 1. This is now known to be false.

References

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VI.2.

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

Crossrefs

Cf. A002321, A059571.

Sequence in context: A108414 A253250 A097477 * A031249 A031232 A362024

Adjacent sequences: A059569 A059570 A059571 * A059573 A059574 A059575

Keyword

nonn

Author

N. J. A. Sloane, Feb 16 2001

Status

approved