

A059581


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


1



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
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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



MATHEMATICA

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


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



