A069158 - OEIS

A069158

a(n) = Product{d|n} mu(d), product over positive divisors, d, of n, where mu(d) = Moebius function (A008683).

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

1,1

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, ...) [R. J. Mathar, Dec 15 2008]

Not multiplicative: For example a(2)*a(15) <> a(30). - R. J. Mathar, Mar 31 2012

Row products of table A225817. - Reinhard Zumkeller, Jul 30 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 0 if mu(n) = 0; a(n) = -1 if n = prime; a(n) = 1 if n = squarefree composite or 1.

EXAMPLE

a(6) = mu(1)*mu(2)*mu(3)*mu(6) = 1*(-1)*(-1)*1 = 1.

MAPLE

A069158 := proc(n)

mul(numtheory[mobius](d), d=numtheory[divisors](n)) ;

end proc: # R. J. Mathar, May 28 2016

MATHEMATICA

a[n_] := Product[MoebiusMu[d], {d, Divisors[n]}]; Array[a, 106] (* Jean-François Alcover, Feb 22 2018 *)

PROG

(Magma) f := function(n); t1 := &*[MoebiusMu(d) : d in Divisors(n) ]; return t1; end function;

(Haskell)

a069158 = product . a225817_row -- Reinhard Zumkeller, Jul 30 2013

CROSSREFS

Sequence in context: A080323 A157657 A359155 * A353559 A253206 A133639

Adjacent sequences: A069155 A069156 A069157 * A069159 A069160 A069161

KEYWORD

sign

AUTHOR

Leroy Quet, Apr 08 2002

STATUS

approved