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 A076544 #24 May 29 2025 06:11:11
%S A076544 2,0,0,-1,0,2,0,-1,-1,2,0,-1,0,2,2,-1,0,-1,0,-1,2,2,0,-1,-1,2,-1,-1,0,
%T A076544 0,0,-1,2,2,2,-1,0,2,2,-1,0,0,0,-1,-1,2,0,-1,-1,-1,2,-1,0,-1,2,-1,2,2,
%U A076544 0,-1,0,2,-1,-1,2,0,0,-1,2,0,0,-1,0,2,-1,-1,2,0,0,-1,-1,2,0,-1,2,2,2,-1,0,-1,2,-1,2,2,2,-1,0,-1,-1,-1
%N A076544 a(n) = mu(n) + sqf(n) where mu(n) is Moebius function, sqf(n) = 1 if n is squarefree and sqf(n) = -1 otherwise.
%H A076544 Antti Karttunen, <a href="/A076544/b076544.txt">Table of n, a(n) for n = 1..10000</a>
%H A076544 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A076544 a(n) = mu(n) + -1^(1+abs(mu(n))), where mu(n) = A008683(n). - _Antti Karttunen_, Jul 26 2017
%F A076544 From _Amiram Eldar_, May 28 2025: (Start)
%F A076544 a(n) = 2*mu(n)^2 + mu(n) - 1, where mu(n) = A008683(n).
%F A076544 Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} = 12/Pi^2 - 1. (End)
%t A076544 ms[n_]:=MoebiusMu[n]+If[SquareFreeQ[n],1,-1]; Array[ms,100] (* _Harvey P. Dale_, Feb 22 2013 *)
%o A076544 (Scheme) (define (A076544 n) (+ (A008683 n) (expt -1 (+ 1 (abs (A008683 n)))))) ;; _Antti Karttunen_, Jul 26 2017
%o A076544 (PARI) a(n) = {my(m = moebius(n)); 2 * m^2 + m - 1;} \\ _Amiram Eldar_, May 28 2025
%Y A076544 Absolute values give A007423.
%Y A076544 Cf. A005117, A008683.
%K A076544 easy,sign
%O A076544 1,1
%A A076544 _Zak Seidov_, Oct 19 2002