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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.)