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.
%I A084237 #40 Feb 16 2025 08:32:49
%S A084237 1,-1,1,2,-23,-48,212,1037,1928,-222,-33722,-87856,62366,599582,
%T A084237 -875575,-3216373,-3195437,-21830254,-46758740,899990187,461113106,
%U A084237 -3395895277,-2061910120,62467771689
%N A084237 a(n) = M(10^n), where M(n) is Mertens's function.
%H A084237 Bernardo Boncompagni, <a href="https://web.archive.org/web/20111009173908/http://mertens.redgolpe.com:80/">Selected values of the Mertens function</a>.
%H A084237 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 A084237 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 A084237 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MertensFunction.html">Mertens Function</a>.
%F A084237 Mertens's function: Sum_{k=1..n} mu(k), where mu = Möbius function (A008683).
%F A084237 a(n) = A002321(10^n).
%t A084237 s = 0; i = 1; Do[ While[i <= 10^n, s = s + MoebiusMu[i]; i++ ]; Print[s], {n, 0, 50}]
%o A084237 (Perl) use ntheory ":all"; say mertens(10**$_) for 0..15; # _Dana Jacobsen_, May 22 2015
%Y A084237 Cf. A002321, A008683.
%K A084237 sign,more
%O A084237 0,4
%A A084237 _Robert G. Wilson v_, May 15 2003
%E A084237 More terms from _Eric W. Weisstein_, Jun 27 2003
%E A084237 a(17) from _Bernardo Boncompagni_, Jul 06 2011
%E A084237 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 A084237 a(21)'s sign correction and a(23) from Helfgott and Thompson (2021) added by _Amiram Eldar_, May 21 2021