%I #18 Mar 19 2017 00:58:44
%S -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,
%T 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,
%U 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
%N From Von Sterneck's conjecture: floor(sqrt(n)) - 2*|Mertens's function A002321(n)|.
%C 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).
%D D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VI.2, p. 188.
%t Table[Floor[Sqrt[n]] - 2 Abs[Plus @@ MoebiusMu[Range[n]]], {n, 1, 80}] (* _Carl Najafi_, Aug 17 2011 *)
%Y Cf. A002321, A059571.
%K sign
%O 1,5
%A _N. J. A. Sloane_, Feb 16 2001