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

1,5

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.

Links

Table of n, a(n) for n=1..93.

Mathematica

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

Crossrefs

Cf. A002321, A059571.

Sequence in context: A158950 A213013 A242667 * A344319 A236998 A297116

Adjacent sequences: A059578 A059579 A059580 * A059582 A059583 A059584

Keyword

sign

Author

N. J. A. Sloane, Feb 16 2001

Status

approved