cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A059581 #18 Mar 19 2017 00:58:44
%S A059581 -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 A059581 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 A059581 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 A059581 From Von Sterneck's conjecture: floor(sqrt(n)) - 2*|Mertens's function A002321(n)|.
%C A059581 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 A059581 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VI.2, p. 188.
%t A059581 Table[Floor[Sqrt[n]] - 2 Abs[Plus @@ MoebiusMu[Range[n]]], {n, 1, 80}] (* _Carl Najafi_, Aug 17 2011 *)
%Y A059581 Cf. A002321, A059571.
%K A059581 sign
%O A059581 1,5
%A A059581 _N. J. A. Sloane_, Feb 16 2001