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A158522
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Dirichlet inverse of number of unitary divisors of n (A034444).
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0
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1, -2, -2, 2, -2, 4, -2, -2, 2, 4, -2, -4, -2, 4, 4, 2, -2, -4, -2, -4, 4, 4, -2, 4, 2, 4, -2, -4, -2, -8, -2, -2, 4, 4, 4, 4, -2, 4, 4, 4, -2, -8, -2, -4, -4, 4, -2, -4, 2, -4, 4, -4, -2, 4, 4, 4, 4, 4, -2, 8, -2, 4, -4, 2, 4, -8, -2, -4, 4, -8, -2, -4, -2, 4, -4, -4, 4, -8, -2, -4, 2, 4, -2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Abs{a(n)} = A034444(n). Examples of Dirichlet convolutions with function a(n), i.e. b(n) = Sum_{d|n} a(d)*c(n/d): a(n) * A034444(n) = A063524(n), a(n) * A000005(n) = A010052(n), a(n) * A000027(n) = A074722(n), a(n) * A000012(n) = A008836(n).
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FORMULA
| a(n) = (-1)^A001222(n)*A034444(n) = (-1)^A001222(n)*2^A001221(n), for n >= 2.
Multiplicative with a(p^e) = 2*(-1)^e, p prime, e>0. a(p^0) = 1.
Dirichlet g.f.: zeta(2s)/(zeta(s))^2. - R. J. Mathar, Apr 02 2011
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EXAMPLE
| a(60) = a(2^2*3*5) = [(-1)^2*2]*[(-1)^1*2]*[(-1)^1*2] = 2*(-2)*(-2) = 8.
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CROSSREFS
| Cf. A034444, A063524, A000005, A010052, A000027, A074722, A001222, A001221, A000040, A006881, A120944, A000961.
Sequence in context: A053238 A058263 A048669 * A034444 A073180 A183095
Adjacent sequences: A158519 A158520 A158521 * A158523 A158524 A158525
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KEYWORD
| sign,mult
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AUTHOR
| Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 20 2009
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