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 A368405 #11 Apr 26 2025 21:36:03
%S A368405 1,0,-1,-2,-3,-2,-3,-2,-3,-2,-3,-2,-3,-2,-1,-2,-3,-2,-3,-2,-1,0,-1,-2,
%T A368405 -3,-2,-1,0,-1,-2,-3,-2,-1,0,1,2,1,2,3,2,1,0,-1,0,1,2,1,2,1,2,3,4,3,2,
%U A368405 3,2,3,4,3,2,1,2,3,4,5,4,3,4,5,4,3,2,1,2,3,4,5
%N A368405 Infinitary version of Mertens's function: a(n) = Sum_{k=1..n} A064179(k).
%H A368405 Amiram Eldar, <a href="/A368405/b368405.txt">Table of n, a(n) for n = 1..10000</a>
%H A368405 Rasa Steuding, Jörn Steuding, and László Tóth, <a href="https://doi.org/10.1007/s12215-011-0022-x">A modified Möbius mu-function</a>, Rendiconti del Circolo Matematico di Palermo, Vol. 60 (2011), pp. 13-21; <a href="https://arxiv.org/abs/1109.4242">arXiv preprint</a>, arXiv:1109.4242 [math.NT], 2011.
%t A368405 f[p_, e_] := (-1)^DigitCount[e, 2, 1]; imu[1] = 1; imu[n_] := Times @@ f @@@ FactorInteger[n]; Accumulate[Array[imu, 100]]
%o A368405 (PARI) imu(n) = vecprod(apply(x -> (-1)^hammingweight(x), factor(n)[, 2]));
%o A368405 lista(nmax) = {my(s = 0); for(k = 1, nmax, s+ = imu(k); print1(s, ", "));}
%Y A368405 Partial sums of A064179.
%Y A368405 Similar sequences: A002321, A174863 (unitary), A209802 (exponential).
%K A368405 sign,easy
%O A368405 1,4
%A A368405 _Amiram Eldar_, Dec 23 2023