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 A028260 Numbers with an even number of prime divisors (counted with multiplicity); numbers k such that the Liouville function lambda(k) (A008836) is positive. 133
 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 k appears, p*k does not (p primes). - Philippe Deléham, Jun 10 2006 The product of any two terms of this sequence, or any two terms of the complement of this sequence (A026424), is a term of this sequence. The product of a term of this sequence and a term of A026424 is a term of A026424. The primitive terms 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, 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,changed AUTHOR Dan Asimov (dan(AT)research.att.com) STATUS approved

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Last modified June 24 05:09 EDT 2021. Contains 345416 sequences. (Running on oeis4.)