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%I #37 May 21 2021 04:14:01
%S 1,0,-1,-2,-1,-4,-1,-2,-1,-4,-4,7,-19,22,-32,26,14,-20,24,-125,257,
%T -362,228,-10,211,-1042,329,330,-1703,6222,-10374,9569,1814,-10339,
%U -3421,8435,38176,-28118,38729,-135944,101597,15295,-169338,259886,-474483,1726370,-3554573
%N a(n) = M(2^n), where M(n) is Mertens's function, A002321.
%H Chai Wah Wu and Amiram Eldar, <a href="/A084236/b084236.txt">Table of n, a(n) for n = 0..75</a> (terms 0..73 from Hurst's paper added by Chai Wah Wu, terms 74..75 from Helfgott and Thompson's paper added by Amiram Eldar)
%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 Greg Hurst, <a href="https://doi.org/10.1090/mcom/3275">Computations of the Mertens function and improved bounds on the Mertens conjecture</a>, Mathematics of Computation, Vol. 87, No. 310 (2018), pp. 1013-1028; <a href="https://arxiv.org/abs/1610.08551">arXiv preprint</a>, arXiv:1610.08551 [math.NT], 2016-2017.
%F a(n) = A002321(2^n).
%F a(n) = Sum_{k=1..2^n} mu(k), where mu = Moebius function (A008683).
%t s = 0; i = 1; Do[ While[i <= 2^n, s = s + MoebiusMu[i]; i++ ]; Print[s], {n, 0, 50}]
%o (PARI) a(n) = sum(k=1, 2^n, moebius(k)) \\ _Indranil Ghosh_, Mar 15 2017
%Y Cf. A000079, A002321, A008683.
%K sign
%O 0,4
%A _Robert G. Wilson v_, May 15 2003
%E a(31)-a(46) from Hurst's paper (copied by _Charles R Greathouse IV_, Oct 15 2018)
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