|
%I #65 Jan 31 2024 08:40:19
%S 1,4,6,9,10,14,15,16,21,22,24,25,26,33,34,35,36,38,39,40,46,49,51,54,
%T 55,56,57,58,60,62,64,65,69,74,77,81,82,84,85,86,87,88,90,91,93,94,95,
%U 96,100,104,106,111,115,118,119,121,122,123,126,129,132,133,134
%N Numbers with an even number of prime divisors (counted with multiplicity); numbers k such that the Liouville function lambda(k) (A008836) is positive.
%C If k appears, p*k does not (p primes). - _Philippe Deléham_, Jun 10 2006
%C 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
%C A072978 is a subsequence. - _Reinhard Zumkeller_, Sep 20 2008
%C Quadratic residues of A191089(n) as n -> oo. - _Travis Scott_, Jan 14 2023
%H T. D. Noe, <a href="/A028260/b028260.txt">Table of n, a(n) for n = 1..10000</a>
%H S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/collectedpapers/Irregular/Irregular1.htm">Irregular numbers</a>, J. Indian Math. Soc., 5 (1913), 105-106; Coll. Papers 20-21.
%F A066829(a(n)) = 0. - _Reinhard Zumkeller_, Jun 26 2009
%F A001222(a(n)) mod 2 = 0. - _Reinhard Zumkeller_, Oct 05 2011
%F Sum_{n>=1} 1/a(n)^s = (zeta(s)^2 + zeta(2*s))/(2*zeta(s)). - _Enrique Pérez Herrero_, Jul 06 2012
%p 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
%t Select[Range[200],EvenQ[PrimeOmega[#]]&] (* _Harvey P. Dale_, Aug 14 2011 *)
%t Select[Range@ 134, LiouvilleLambda@# > 0 &] (* _Robert G. Wilson v_, Jul 06 2012 *)
%o (Haskell)
%o a028260 n = a028260_list !! (n-1)
%o a028260_list = filter (even . a001222) [1..]
%o -- _Reinhard Zumkeller_, Oct 05 2011
%o (PARI) is(n)=bigomega(n)%2==0 \\ _Charles R Greathouse IV_, May 29 2013
%Y Cf. A001222, A001358, A008836, A026424 (complement), A145784, A065043 (char. func).
%K nonn,easy,nice
%O 1,2
%A Dan Asimov (dan(AT)research.att.com)
|
