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A157657
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a(1) = 1, a(n) = (-1)*mu(n) for n >= 2.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(1) = 1, a(n) = (-1)*A008683(n) for n >= 2. a(1) = 1, a(n)=(-1)^(k + 1) if n is the product of k distinct primes, otherwise a(n)=0. Sum_{d|n} a(d) = 1 if n = 1 else 2. a(1) = 1, 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). Examples of Dirichlet convolutions with function a(n), i.e. b(n) = Sum_{d|n} a(d)*c(n/d): a(n) * A000012(n) = A130130(n), a(n) * A000027(n) = A053158(n).
Apparently the Dirichlet inverse of A114006. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2010]
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CROSSREFS
| Cf. A000040, A006881, A120944, A000961, A000027, A130130, A053158
Sequence in context: A174600 A075437 A130047 * A008683 A008966 A080323
Adjacent sequences: A157654 A157655 A157656 * A157658 A157659 A157660
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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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