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 A162511 Multiplicative function with a(p^e)=(-1)^(e-1) 7
 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(A162644(n)) = +1; a(A162645(n)) = -1. [Reinhard Zumkeller, Jul 08 2009] LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 G. P. Michon, Multiplicative functions FORMULA Multiplicative function with a(p^e)=(-1)^(e-1) for any prime p and any positive exponent e. a(n) = (-1)^(A001222(n)-A001221(n)). - Reinhard Zumkeller, Jul 08 2009 a(n) = A076479(n) * A008836(n). - R. J. Mathar, Mar 30 2011 EXAMPLE a(n)=1 when n is a squarefree number (A005117). MAPLE A162511 := proc(n)     local a, f;     a := 1;     for f in ifactors(n)[2] do         a := a*(-1)^(op(2, f)-1) ;     end do:     return a; end proc: # R. J. Mathar, May 20 2017 MATHEMATICA a[n_] := (-1)^(PrimeOmega[n] - PrimeNu[n]); Array[a, 100] (* Jean-François Alcover, Apr 24 2017, after Reinhard Zumkeller *) PROG (PARI) a(n)=my(f=factor(n)[, 2]); prod(i=1, #f, -(-1)^f[i]) \\ Charles R Greathouse IV, Mar 09 2015 (Python) from sympy import factorint from operator import mul def a(n):     f=factorint(n)     return 1 if n==1 else reduce(mul, [(-1)**(f[i] - 1) for i in f]) # Indranil Ghosh, May 20 2017 CROSSREFS Cf. A076479, A162510, A162512, A002035, A072587, A036537, A162643, A046660. Sequence in context: A000012 A216430 A232544 * A157895 A063747 A077008 Adjacent sequences:  A162508 A162509 A162510 * A162512 A162513 A162514 KEYWORD easy,mult,sign AUTHOR Gerard P. Michon, Jul 05 2009 STATUS approved

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)