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A065043 Characteristic function of the numbers with an even number of prime factors (counted with multiplicity): a(n) = 1 if n = A028260(k) for some k then 1 else 0. 7
1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for characteristic functions

FORMULA

a(n) = 1 - A001222(n) mod 2.

a(n) = A007421(n) - 1.

a(n) = 1 - A066829(n).

a(n) = (A008836(n) + 1)/2. - Enrique Pérez Herrero, Jul 07 2012

a(n) = A001222(2n) mod 2. - Wesley Ivan Hurt, Jun 22 2013

G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = Sum_{n>=1} x^(n^2)/(1 - x^n). - Ilya Gutkovskiy, Apr 25 2017

MAPLE

A065043 := proc(n)

    if type(numtheory[bigomega](n), 'even') then

        1;

    else

        0;

    end if;

end proc: # R. J. Mathar, Jun 26 2013

MATHEMATICA

Table[(LiouvilleLambda[n]+1)/2, {n, 1, 20}] (* Enrique Pérez Herrero, Jul 07 2012 *)

PROG

(PARI) { for (n=1, 1000, a=1 - bigomega(n)%2; write("b065043.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 04 2009

CROSSREFS

a(A028260(k)) = 1 and a(A026424(k)) = 0 for all k.

A007421(n) - 1.

Cf. A066829, A008836.

Sequence in context: A285076 A267598 A194681 * A189298 A288375 A121559

Adjacent sequences:  A065040 A065041 A065042 * A065044 A065045 A065046

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 05 2001

EXTENSIONS

Corrected by Charles R Greathouse IV, Sep 02 2009

STATUS

approved

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Last modified November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)