A157657 a(1) = 1, a(n) = -mu(n) for n >= 2.

1, 1, 1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 1, -1, -1, 0, 1, 0, 1, 0, -1, -1, 1, 0, 0, -1, 0, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, -1, -1, 0, 1, 1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, 0, -1, 0, -1, -1, 1, 0, 1, -1, 0, 0, -1, 1, 1, 0, -1, 1, 1, 0, 1, -1, 0, 0, -1, 1, 1, 0, 0, -1, 1, 0, -1, -1, -1, 0, 1, 0, -1, 0, -1, -1, -1, 0, 1, 0, 0, 0

Offset: 1

Author

Jaroslav Krizek, Mar 03 2009

Keywords

• sign

Comments

Apparently the Dirichlet inverse of A114006. [R. J. Mathar, Jul 15 2010]

Not multiplicative; for example a(2)*a(3) != a(6). - R. J. Mathar, Mar 31 2012

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A008683, A157658 (same except for a(1)).

Programs

Mathematica

a[1]:=1; a[n_]:=-MoebiusMu[n]; Array[a,100] (* Stefano Spezia, May 03 2025 *)

PARI

a(n)=if(n==1,1, -moebius(n)); \\ Joerg Arndt, Aug 25 2014

Scheme

(define (A157657 n) (if (= 1 n) 1 (- (A008683 n)))) ;; Antti Karttunen, Jul 26 2017

Extensions

Added more terms, Joerg Arndt, Aug 25 2014