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A069158
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a(n) = Product{d|n} mu(d), product over positive divisors, d, of n, where mu(d) = Moebius function (A008683).
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3
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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, 1, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, 1, 0, 0, 1, 1, -1, 0, 1, 1, -1, 0, -1, 1, 0, 0, 1, 1, -1, 0, 0, 1, -1, 0, 1, 1, 1, 0, -1, 0, 1, 0, 1, 1, 1, 0, -1, 0, 0, 0, -1, 1, -1, 0, 1, 1
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OFFSET
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1,1
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COMMENTS
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Absolute value of a(n) = absolute value of mu(n).
Differs from A080323 at n=2, 105, 165, 195, 231, ..., 15015,..., 19635,.. (cf. A046389, A046391, ...) [R. J. Mathar, Dec 15 2008]
Not multiplicative: For example a(2)*a(15) <> a(30). - R. J. Mathar, Mar 31 2012
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LINKS
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FORMULA
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a(n) = 0 if mu(n) = 0; a(n) = -1 if n = prime; a(n) = 1 if n = squarefree composite or 1.
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EXAMPLE
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a(6) = mu(1)*mu(2)*mu(3)*mu(6) = 1*(-1)*(-1)*1 = 1.
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MAPLE
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mul(numtheory[mobius](d), d=numtheory[divisors](n)) ;
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MATHEMATICA
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PROG
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(Magma) f := function(n); t1 := &*[MoebiusMu(d) : d in Divisors(n) ]; return t1; end function;
(Haskell)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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