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A069158
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Product{d|n} mu(d), product over positive divisors, d, of n, where mu(d) = Moebius function (A008683).
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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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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, ...) [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 15 2008]
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FORMULA
| 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
| a(6) = mu(1)*mu(2)*mu(3)*mu(6) = 1*(-1)*(-1)*1 = 1.
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PROG
| (MAGMA) f := function(n); t1 := &*[MoebiusMu(d) : d in Divisors(n) ]; return t1; end function;
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CROSSREFS
| Sequence in context: A008683 A008966 A080323 * A133639 A060038 A167021
Adjacent sequences: A069155 A069156 A069157 * A069159 A069160 A069161
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KEYWORD
| sign
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AUTHOR
| Leroy Quet, Apr 08 2002
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