A065043 - OEIS

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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.

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`
	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) ) } [From 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: A173858 A101266 A105367 * A121559 A004641 A100810` `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 May 25 19:47 EDT 2013. Contains 225649 sequences.