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 A026424 Number of prime divisors (counted with multiplicity) is odd; Liouville function lambda(n) (A008836) is negative. 47
 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 Lexicographically earliest sequence of distinct nonnegative integers with no term being the product of any two not necessarily distinct terms. The equivalent sequence for addition/subtraction is A005408 (the odd numbers), for exponentiation is A259444, and for binary exclusive OR is A000069. - Peter Munn, Mar 16 2018 The equivalent lexicographically earliest sequence with no term being the product of any two distinct terms is A026416. A000028 is similarly the equivalent sequence when A059897 is used as multiplicative operator in place of standard integer multiplication. - Peter Munn, Mar 16 2019 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 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 MAPLE isA026424 := proc(n)     if type(numtheory[bigomega](n) , 'odd') then         true;     else         false;     end if; end proc: A026424 := proc(n)     option remember;     if n =1 then         2;     else         for a from procname(n-1)+1 do             if isA026424(a) then                 return a;             end if;         end do:     end if; end proc: # R. J. Mathar, May 25 2017 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-François 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. Cf. A026416 and cross-references therein. Cf. A000028, A000069, A005408, A259444. Sequence in context: A245303 A166982 A026422 * A298207 A229125 A228853 Adjacent sequences:  A026421 A026422 A026423 * A026425 A026426 A026427 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified October 23 14:29 EDT 2019. Contains 328345 sequences. (Running on oeis4.)