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a(1) = 1, a(n) = -mu(n) for n >= 2.
3

%I #19 Jul 26 2017 09:23:51

%S 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,

%T 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,

%U 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

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

%C Apparently the Dirichlet inverse of A114006. [_R. J. Mathar_, Jul 15 2010]

%C Not multiplicative; for example a(2)*a(3) != a(6). - _R. J. Mathar_, Mar 31 2012

%H Antti Karttunen, <a href="/A157657/b157657.txt">Table of n, a(n) for n = 1..5000</a>

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

%o (PARI) a(n)=if(n==1,1, -moebius(n)); \\ _Joerg Arndt_, Aug 25 2014

%o (Scheme) (define (A157657 n) (if (= 1 n) 1 (- (A008683 n)))) ;; _Antti Karttunen_, Jul 26 2017

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

%K sign

%O 1,1

%A _Jaroslav Krizek_, Mar 03 2009

%E Added more terms, _Joerg Arndt_, Aug 25 2014