

A028260


Numbers n such that number of prime divisors of n (counted with multiplicity) is even; Liouville function lambda(n) (A008836) is positive.


52



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
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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. AdamsWatters, 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), 105106; Coll. Papers 2021.


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(n1)+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 !! (n1)
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



