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A157658
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a(1) = 0, a(n) = (-1)*mu(n) for n >= 2.
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1
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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, -1, -1, -1, 0, 1, -1, -1, 0, 1, 1, 1, 0, 0, -1, 1, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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).
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FORMULA
| a(n)=A157657(n), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 08 2009]
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PROG
| (PARI) a(n)=if(n>1, -moebius(n), 0) \\ Charles R Greathouse IV, Dec 19 2011
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CROSSREFS
| Cf. A000040, A006881, A120944, A000961, A000027, A130130, A053158, A051953, A000203, A001065, A000005, A032741, A000012, A057427, A008683, A057427, A007427, A032741.
Sequence in context: A163532 A014578 A030190 * A123506 A051105 A155897
Adjacent sequences: A157655 A157656 A157657 * A157659 A157660 A157661
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KEYWORD
| sign
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AUTHOR
| Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 03 2009
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