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

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, 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, 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

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = mu(n) + -1^(1+abs(mu(n))), where mu(n) = A008683(n). - Antti Karttunen, Jul 26 2017

Mathematica

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

Prog

(Scheme) (define (A076544 n) (+ (A008683 n) (expt -1 (+ 1 (abs (A008683 n)))))) ;; Antti Karttunen, Jul 26 2017

Crossrefs

Absolute values give A007423.

Cf. A008683.

Sequence in context: A321445 A353459 A007423 * A349912 A345079 A307377

Adjacent sequences: A076541 A076542 A076543 * A076545 A076546 A076547

Keyword

easy,sign

Author

Zak Seidov, Oct 19 2002

Status

approved