A059581 From Von Sterneck's conjecture: floor(sqrt(n)) - 2*|Mertens's function A002321(n)|.

-1, 1, -1, 0, -2, 0, -2, -2, -1, 1, -1, -1, -3, -1, 1, 2, 0, 0, -2, -2, 0, 2, 0, 0, 1, 3, 3, 3, 1, -1, -3, -3, -1, 1, 3, 4, 2, 4, 6, 6, 4, 2, 0, 0, 0, 2, 0, 0, 1, 1, 3, 3, 1, 1, 3, 3, 5, 7, 5, 5, 3, 5, 5, 6, 8, 6, 4, 4, 6, 4, 2, 2, 0, 2, 2, 2, 4, 2, 0, 0, 1, 3, 1, 1, 3, 5, 7, 7, 5, 5, 7, 7, 9

Offset: 1

Author

N. J. A. Sloane, Feb 16 2001

Keywords

• sign

Comments

Von Sterneck conjectured that 2*|A002321(n)| < sqrt(n) for all sufficiently large n. This is now known to be false. This is different from the Mertens conjecture that |A002321(n)| < sqrt(n) for all n > 1 (which is also false).

References

• D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VI.2, p. 188.

Crossrefs

Cf. A002321, A059571.

Programs

Mathematica

Table[Floor[Sqrt[n]] - 2 Abs[Plus @@ MoebiusMu[Range[n]]], {n, 1, 80}] (* Carl Najafi, Aug 17 2011 *)