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%I #39 May 21 2021 04:14:08
%S 1,-1,1,2,-23,-48,212,1037,1928,-222,-33722,-87856,62366,599582,
%T -875575,-3216373,-3195437,-21830254,-46758740,899990187,461113106,
%U -3395895277,-2061910120,62467771689
%N a(n) = M(10^n), where M(n) is Mertens's function.
%H Bernardo Boncompagni, <a href="https://web.archive.org/web/20111009173908/http://mertens.redgolpe.com:80/">Selected values of the Mertens function</a>.
%H Eugene Kuznetsov, <a href="http://arxiv.org/abs/1108.0135">Computing the Mertens function on a GPU</a>, arXiv:1108.0135 [math.NT], 2011.
%H Harald A. Helfgott and Lola Thompson, <a href="https://arxiv.org/abs/2101.08773">Summing mu(n): a faster elementary algorithm</a>, arXiv:2101.08773 [math.NT], 2021.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MertensFunction.html">Mertens Function</a>.
%F Mertens's function: Sum_{k=1..n} mu(k), where mu = Möbius function (A008683).
%F a(n) = A002321(10^n).
%t s = 0; i = 1; Do[ While[i <= 10^n, s = s + MoebiusMu[i]; i++ ]; Print[s], {n, 0, 50}]
%o (Perl) use ntheory ":all"; say mertens(10**$_) for 0..15; # _Dana Jacobsen_, May 22 2015
%Y Cf. A002321, A008683.
%K sign,more
%O 0,4
%A _Robert G. Wilson v_, May 15 2003
%E More terms from _Eric W. Weisstein_, Jun 27 2003
%E a(17) from _Bernardo Boncompagni_, Jul 06 2011
%E Corrected a(17) and added a(18)-a(22) from Eugene Kuznetsov, a(17)-a(19) independently confirmed by _Richard Sladkey_, Aug 28 2012
%E a(21)'s sign correction and a(23) from Helfgott and Thompson (2021) added by _Amiram Eldar_, May 21 2021
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