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A158522
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Dirichlet inverse of number of unitary divisors of n (A034444).
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2
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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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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
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a(60) = a(2^2*3*5) = [(-1)^2*2]*[(-1)^1*2]*[(-1)^1*2] = 2*(-2)*(-2) = 8.
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MATHEMATICA
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Table[LiouvilleLambda[n] 2^PrimeNu[n], {n, 1, 50}] (* Geoffrey Critzer, Mar 07 2015 *)
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PROG
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(PARI) for(n=1, 20, print1((-1)^bigomega(n)* 2^omega(n), ", ")) \\ G. C. Greubel, May 21 2017
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CROSSREFS
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Cf. A034444, A063524, A000005, A010052, A000027, A074722, A001222, A001221, A000040, A006881, A120944, A000961.
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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