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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Neither this sequence nor its complement (A028260) contains any infinite arithmetic progression. - Franklin T. Adams-Watters, 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), 105-106; Coll. Papers 20-21.

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)^2-zeta(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 &] (* Jean-Fran├žois Alcover, Aug 19 2013 *)

PROG

(Haskell)

a026424 n = a026424_list !! (n-1)

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

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Last modified February 10 20:58 EST 2016. Contains 268157 sequences.