%I A157658
%S A157658 0,1,1,0,1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,
%T A157658 1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0
%V A157658 0,1,1,0,1,-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,
%W A157658 -1,-1,-1,0,1,-1,-1,0,1,1,1,0,0,-1,1,0,0,0
%N A157658 a(1) = 0, a(n) = (-1)*mu(n) for n >= 2.
%C A157658 a(1) = 0, a(n) = (-1)*A008683(n) for n >= 2. a(1) = 0, a(n)=(-1)^(k + 
               1)if n is the product of k distinct primes, otherwise a(n)=0. Sum_{d|n} 
               a(d) = 0 if n = 1 else 1. a(1) = 0, a(p) = 1, a(pq) = -1, a(pq...z) 
               = (-1)^(k + 1), a(p^k) = 0, for k = natural numbers (A000027)(n) 
               for n > 2, p = primes (A000040), pq = product of two distinct primes 
               (A006881), pq...z = product of k (k > 2) distinct primes p, q, ..., 
               z (A120944), p^k = prime powers (A000961(n) for n > 1). a(n) for 
               n >= 1 is Dirichlet convolution of following functions b(n), c(n), 
               a(n) = Sum_{d|n} b(d)*c(n/d)): a(n) = A008683(n) * A057427(n-1), 
               a(n) = A007427(n) * A032741(n). Examples of Dirichlet convolutions 
               with function a(n), i.e. b(n) = Sum_{d|n} a(d)*c(n/d): a(n) * A000027(n) 
               = A051953(n), a(n) * A000203(n) = A001065(n), a(n) * A000005(n) = 
               A032741(n), a(n) * A000012(n) = A057427(n-1).
%F A157658 a(n)=A157657(n), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 08 2009]
%Y A157658 Cf. A000040, A006881, A120944, A000961, A000027, A130130, A053158, A051953, 
               A000203, A001065, A000005, A032741, A000012, A057427, A008683, A057427, 
               A007427, A032741.
%Y A157658 Sequence in context: A163532 A014578 A030190 this_sequence A123506 A051105 
               A155897
%Y A157658 Adjacent sequences: A157655 A157656 A157657 this_sequence A157659 A157660 
               A157661
%K A157658 sign
%O A157658 1,1
%A A157658 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 03 2009