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 A053866 Parity of A000203(n), the sum of the divisors of n; a(n) = 1 when n is a square or twice a square, 0 otherwise. 34
 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also parity of A001227, the number of odd divisors of n. - Omar E. Pol, Apr 04 2016 Also parity of A000593, the sum of odd divisors of n. - Omar E. Pol, Apr 05 2016 Characteristic function of A028982. - Antti Karttunen, Sep 25 2017 It appears that this is also the parity of A067742, the number of middle divisors of n. - Omar E. Pol, Mar 18 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65536 J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, 2012. J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, J. Int. Seq. 16 (2013) #13.1.8. Michael Gilleland, Some Self-Similar Integer Sequences FORMULA a(n) = A000203(n) mod 2. a(n)=1 iff n>0 is a square or twice a square. Multiplicative with a(2^e)=1, a(p^e)=1 if e even, 0 otherwise. a(n) = A093709(n) if n>0. Dirichlet g.f.: zeta(2s)(1+2^-s). - Michael Somos, Apr 12 2004 a(n) = A001157(n) mod 2. - R. J. Mathar, Apr 02 2011 a(n) = floor(sqrt(n)) + floor(sqrt(n/2)) - floor(sqrt(n-1))-floor(sqrt((n-1)/2)). - Enrique Pérez Herrero, Oct 15 2013 a(n) = A000035(A000203(n)). - Omar E. Pol, Oct 26 2013 a(n) = A063524(A286357(n)) = A063524(A292583(n)). - Antti Karttunen, Sep 25 2017 a(n) = A295896(A156552(n)). - Antti Karttunen, Dec 02 2017 a(n) = Sum_{ m: m^2|n } A019590(n/m^2). - Andrey Zabolotskiy, May 07 2018 G.f.: (theta_3(x) + theta_3(x^2))/2 - 1. - Ilya Gutkovskiy, May 23 2019 MAPLE A053866:= (n -> numtheory[sigma](n) mod 2): seq (A053866(n), n=0..104); # Jani Melik, Jan 28 2011 MATHEMATICA Mod[DivisorSigma[1, Range[110]], 2] (* Harvey P. Dale, Sep 04 2017 *) PROG (PARI) {a(n) = if( n<1, 0, issquare(n) || issquare(2*n))} /* Michael Somos, Apr 12 2004 */ CROSSREFS Essentially same as A093709. Cf. A000203, A000593, A001227, A028982, A286357, A292583, A295896, A019590, A025441, A145393. Sequence in context: A297054 A266459 A214509 * A143259 A207710 A207735 Adjacent sequences:  A053863 A053864 A053865 * A053867 A053868 A053869 KEYWORD nonn,mult AUTHOR Henry Bottomley, Mar 29 2000 EXTENSIONS More terms from James A. Sellers, Apr 08 2000 Alternative description added to the name by Antti Karttunen, Sep 25 2017 STATUS approved

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)