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%I #42 Mar 03 2022 10:11:57
%S 0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,
%T 1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,
%U 1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1
%N Characteristic function of numbers that are not multiples of 9.
%H Antti Karttunen, <a href="/A168182/b168182.txt">Table of n, a(n) for n = 0..999</a>
%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/rfmc.txt">Rational Function Multiplicative Coefficients</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).
%F Euler transform of length 9 sequence [1, 0, 0, 0, 0, 0, 0, -1, 1]. - _Michael Somos_, Mar 22 2011
%F Moebius transform is length 9 sequence [1, 0, 0, 0, 0, 0, 0, 0, -1]. - _Michael Somos_, Mar 22 2011
%F Expansion of x * (1 - x^8) / ((1 - x) * (1 - x^9)) in powers of x. - _Michael Somos_, Mar 22 2011
%F Multiplicative with a(p^e) = (if p=3 then 0^(e-1) else 1), p prime and e>0.
%F a(n) = a(n+9) = a(-n) for all n in Z.
%F a(n) = A000007(A010878(n)).
%F a(A168183(n)) = 1. a(A008591(n)) = 0.
%F A033441(n) = Sum_{k=0..n} a(k)*(n-k).
%F G.f.: -x*(1+x)*(1+x^2)*(1+x^4) / ( (x-1)*(1+x+x^2)*(x^6+x^3+1) ). - _R. J. Mathar_, Jan 07 2011
%F Dirichlet g.f. (1-3^(-2s))*zeta(s). - _R. J. Mathar_, Mar 06 2011
%F For the general case: the characteristic function of numbers that are not multiples of m is a(n)=floor((n-1)/m)-floor(n/m)+1, m,n > 0. - _Boris Putievskiy_, May 08 2013
%F a(n) = 1 - A267142(n). - _Antti Karttunen_, Oct 07 2017
%e G.f. = x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^10 + x^11 + x^12 + x^13 + ...
%t A168182[n_]:=Boole[!Divisible[n,9]]; Array[A168182, 10, 0]
%o (PARI) {a(n) = sign(n%9)}; /* _Michael Somos_, Mar 22 2011 */
%Y Cf. A168185, A145568, A168184, A168181, A109720, A097325, A011558, A166486, A011655, A000035, A267142, A033441.
%K easy,mult,nonn
%O 0,1
%A _Reinhard Zumkeller_, Nov 30 2009
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