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A076544 mu(n)+sqf(n): mu(n) is Moebius function; sqf(n)=1 if n is squarefree, sqf(n)=-1 otherwise. 1

%I

%S 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 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 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 mu(n)+sqf(n): mu(n) is Moebius function; sqf(n)=1 if n is squarefree, sqf(n)=-1 otherwise.

%H Antti Karttunen, <a href="/A076544/b076544.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = mu(n) + -1^(1+abs(mu(n))), where mu(n) = A008683(n). - _Antti Karttunen_, Jul 26 2017

%t ms[n_]:=MoebiusMu[n]+If[SquareFreeQ[n],1,-1]; Array[ms,100] (* _Harvey P. Dale_, Feb 22 2013 *)

%o (Scheme) (define (A076544 n) (+ (A008683 n) (expt -1 (+ 1 (abs (A008683 n)))))) ;; _Antti Karttunen_, Jul 26 2017

%Y Absolute values give A007423.

%Y Cf. A008683.

%K easy,sign

%O 1,1

%A _Zak Seidov_, Oct 19 2002

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)