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A028260 Numbers n such that number of prime divisors of n (counted with multiplicity) is even; Liouville function lambda(n) (A008836) is positive. 44
1, 4, 6, 9, 10, 14, 15, 16, 21, 22, 24, 25, 26, 33, 34, 35, 36, 38, 39, 40, 46, 49, 51, 54, 55, 56, 57, 58, 60, 62, 64, 65, 69, 74, 77, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 95, 96, 100, 104, 106, 111, 115, 118, 119, 121, 122, 123, 126, 129, 132, 133, 134 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If n appears, p*n does not (p primes). - Philippe Deléham, Jun 10 2006

The product of any two members of this sequence, or any two members of the complement of this sequence (A026424) is a member of this sequence. The product of a member of this sequence and a member of A026424 is a member of A026424. The primitive elements of this sequence are the semiprimes (A001358). - Franklin T. Adams-Watters, Nov 27 2006

A072978 is a subsequence. - Reinhard Zumkeller, Sep 20 2008

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

S. Ramanujan, Irregular numbers, J. Indian Math. Soc., 5 (1913), 105-106; Coll. Papers 20-21.

FORMULA

A066829(a(n)) = 0. - Reinhard Zumkeller, Jun 26 2009

A001222(a(n)) mod 2 = 0. - Reinhard Zumkeller, Oct 05 2011

Dirichlet g.f. of A065043: Sum_{n>=1} 1/a(n)^s = (Zeta(s)^2 + Zeta(2*s))/(2*Zeta(s)). - Enrique Pérez Herrero, Jul 06 2012

MAPLE

with(numtheory); A028260 := proc(n) option remember: local k: if(n=1)then return 1: fi: for k from procname(n-1)+1 do if(bigomega(k) mod 2=0)then return k: fi: od: end: seq(A028260(n), n=1..63); # Nathaniel Johnston, May 27 2011

MATHEMATICA

Select[Range[200], EvenQ[PrimeOmega[#]]&] (* Harvey P. Dale, Aug 14 2011 *)

Select[Range@ 134, LiouvilleLambda@# > 0 &] (* Robert G. Wilson v, Jul 06 2012 *)

PROG

(Haskell)

a028260 n = a028260_list !! (n-1)

a028260_list = filter (even . a001222) [1..]

-- Reinhard Zumkeller, Oct 05 2011

(PARI) is(n)=bigomega(n)%2==0 \\ Charles R Greathouse IV, May 29 2013

CROSSREFS

Cf. A001222, A001358, A008836, A026424 (complement), A145784.

Sequence in context: A189300 A300079 A233182 * A085155 A219786 A302038

Adjacent sequences:  A028257 A028258 A028259 * A028261 A028262 A028263

KEYWORD

nonn,easy,nice

AUTHOR

Dan Asimov (dan(AT)research.att.com)

STATUS

approved

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Last modified December 11 03:29 EST 2018. Contains 318049 sequences. (Running on oeis4.)