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 A066829 1 if product of odd number of primes; 0 if product of even number of primes. 20
 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(A026424(n)) = 1; a(A028260(n)) = 0. Contribution from Reinhard Zumkeller, Jul 01 2009: (Start) The first N Terms are constructed by the following sieving process: for j:=1 until N do a(j):=0, for i:=1 until N/2 do for j:=2*i step i until N do a(j):=1-a(i). (End) REFERENCES Cf. A065043. LINKS Reinhard Zumkeller, 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 (provides Dirichlet g.f.) Index entries for sequences generated by sieves [From Reinhard Zumkeller, Jul 01 2009] FORMULA a(n) = (A008836(n) - 1) / 2. a(m*n) = a(m) XOR a(n). [Reinhard Zumkeller, Aug 28 2008] a(n) = A001222(n) mod 2. [Reinhard Zumkeller, Nov 19 2011] EXAMPLE Contribution from Reinhard Zumkeller, Jul 01 2009: (Start) Sieve for N = 30, also demonstrating the affinity to the Sieve of Eratosthenes: [initial] a(j):=0, 1<=j<=30: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 [i=1] a(1)=0 --> a(j):=1, 2<=j<=30: 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [i=2] a(2)=1 --> a(2*j):=0, 2<=j<=[30/2]: 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 [i=3] a(3)=1 --> a(3*j):=0, 2<=j<=[30/3]: 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 [i=4] a(4)=0 --> a(4*j):=1, 2<=j<=[30/4]: 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 [i=5] a(5)=1 --> a(5*j):=0, 2<=j<=[30/5]: 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 [i=6] a(6)=0 --> a(6*j):=1, 2<=j<=[30/6]: 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 [i=7] a(7)=1 --> a(7*j):=0, 2<=j<=[30/7]: 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 [i=8] a(8)=1 --> a(8*j):=0, 2<=j<=[30/8]: 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 [i=9] a(9)=0 --> a(9*j):=1, 2<=j<=[30/9]: 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 [i=10] a(10)=0 --> a(10*j):=1, 2<=j<=[30/10]: 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 1 and so on: a(22):=0 in [i=11], a(24):=0 in [i=12], a(26):=0 in [i=13], a(28):=1 in [i=14], and a(30):=1 in [i=15]. (End) MAPLE A066829 := proc(n)     modp(numtheory[bigomega](n) , 2) ; end proc: seq(A066829(n), n=1..80) ; # R. J. Mathar, Jul 15 2017 MATHEMATICA Table[(1-LiouvilleLambda[n])/2, {n, 1, 20}] (* Enrique Pérez Herrero, Jul 07 2012 *) Table[If[OddQ[PrimeOmega[n]], 1, 0], {n, 120}] (* Harvey P. Dale, Mar 12 2016 *) PROG (PARI) A066829(n)=if(bigomega(n)%2==1, 1, 0) (Haskell) a066829 = (`mod` 2) . a001222 -- Reinhard Zumkeller, Nov 19 2011 CROSSREFS Cf. A065043. Cf. A072203, A055038 (partial sums), A001222. Sequence in context: A189687 A284653 A099104 * A194664 A285975 A213729 Adjacent sequences:  A066826 A066827 A066828 * A066830 A066831 A066832 KEYWORD nonn,easy AUTHOR G. L. Honaker, Jr., Jan 17 2002 EXTENSIONS Corrected and comment added by Reinhard Zumkeller, Jun 26 2009 STATUS approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)