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A162512 Dirichlet inverse of A162511. 3
1, -1, -1, 2, -1, 1, -1, -4, 2, 1, -1, -2, -1, 1, 1, 8, -1, -2, -1, -2, 1, 1, -1, 4, 2, 1, -4, -2, -1, -1, -1, -16, 1, 1, 1, 4, -1, 1, 1, 4, -1, -1, -1, -2, -2, 1, -1, -8, 2, -2, 1, -2, -1, 4, 1, 4, 1, 1, -1, 2, -1, 1, -2, 32, 1, -1, -1, -2, 1, -1, -1, -8, -1, 1, -2, -2, 1, -1, -1, -8, 8, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The absolute value of this sequence is A162510.

The Moebius function (A008683) can be defined in terms of this sequence: A008683(n) is equal to a(n) if a(n) is odd and zero otherwise.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

G. P. Michon, Multiplicative functions

FORMULA

Multiplicative function with a(p^e)=-(-2)^(e-1) for any prime p and any positive exponent e.

EXAMPLE

a(n) = n/2 when n is a power of 4 (A000302).

a(n) = A008683(n) when n is a squarefree number (A005117).

MAPLE

A162512 := proc(n)

    local a, f;

    a := 1;

    for f in ifactors(n)[2] do

        a := -a*(-2)^(op(2, f)-1) ;

    end do:

    return a;

end proc:

seq(A162512(n), n=1..100) ; # R. J. Mathar, May 20 2017

PROG

(PARI) a(n) = my(f=factor(n)); for(i=1, #f~, f[i, 1]=-(-2)^(f[i, 2]-1); f[i, 2]=1); factorback(f); \\ Michel Marcus, May 20 2017

(Python)

from sympy import factorint

from operator import mul

def a(n):

    f=factorint(n)

    return 1 if n==1 else reduce(mul, [-(-2)**(f[i] - 1) for i in f]) # Indranil Ghosh, May 20 2017

(Scheme) (define (A162512 n) (if (= 1 n) n (* (- (expt -2 (- (A067029 n) 1))) (A162512 (A028234 n))))) ;; Antti Karttunen, May 20 2017, after the given multiplicative formula.

CROSSREFS

Cf. A005117, A008683, A067029, A076479, A162150, A162511

Sequence in context: A252890 A173398 A104404 * A162510 A235388 A252733

Adjacent sequences:  A162509 A162510 A162511 * A162513 A162514 A162515

KEYWORD

easy,mult,sign,changed

AUTHOR

Gerard P. Michon, Jul 05 2009, Jul 06 2009

STATUS

approved

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Last modified May 27 22:57 EDT 2017. Contains 287210 sequences.