

A026424


Number of prime divisors (counted with multiplicity) is odd; Liouville function lambda(n) (A008836) is negative.


31



2, 3, 5, 7, 8, 11, 12, 13, 17, 18, 19, 20, 23, 27, 28, 29, 30, 31, 32, 37, 41, 42, 43, 44, 45, 47, 48, 50, 52, 53, 59, 61, 63, 66, 67, 68, 70, 71, 72, 73, 75, 76, 78, 79, 80, 83, 89, 92, 97, 98, 99, 101, 102, 103, 105, 107, 108, 109, 110, 112
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OFFSET

1,1


COMMENTS

Neither this sequence nor its complement (A028260) contains any infinite arithmetic progression.  Franklin T. AdamsWatters, Sep 05 2008
A066829(a(n)) = 1.  Reinhard Zumkeller, Jun 26 2009
These numbers can be generated by the sieving process described in A066829.  Reinhard Zumkeller, Jul 01 2009


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.
Eric Weisstein's World of Mathematics, Prime Sums
Index entries for sequences generated by sieves  Reinhard Zumkeller, Jul 01 2009


FORMULA

Sum 1/a(n)^m = (zeta(m)^2zeta(2m))/(2*zeta(m)), Dirichlet g.f. of A066829.  Ramanujan.
n>=2 is in sequence if n is not the product of two smaller elements.  David W. Wilson, May 06 2005
A001222(a(n)) mod 2 = 1.  Reinhard Zumkeller, Oct 05 2011
Union of A000040, A014612, A014614, A046308 etc.  R. J. Mathar, Jul 09 2012


MATHEMATICA

Select[Range[2, 112], OddQ[Total[FactorInteger[#]][[2]]] &] (* T. D. Noe, May 07 2011 *)
(* From version 7 on *) Select[Range[2, 112], LiouvilleLambda[#] == 1 &] (* JeanFrançois Alcover, Aug 19 2013 *)


PROG

(Haskell)
a026424 n = a026424_list !! (n1)
a026424_list = filter (odd . a001222) [1..]
 Reinhard Zumkeller, Oct 05 2011
(PARI) is(n)=bigomega(n)%2 \\ Charles R Greathouse IV, Sep 16 2015


CROSSREFS

Cf. A008836, A028260 (complement).
Apart from initial term, same as A026422.
Sequence in context: A245303 A166982 A026422 * A229125 A228853 A141832
Adjacent sequences: A026421 A026422 A026423 * A026425 A026426 A026427


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane.


STATUS

approved



