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 A168182 Characteristic function of numbers that are not multiples of 9. 16
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Antti Karttunen, Table of n, a(n) for n = 0..999 Michael Somos, Rational Function Multiplicative Coefficients Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1). FORMULA Euler transform of length 9 sequence [1, 0, 0, 0, 0, 0, 0, -1, 1]. - Michael Somos, Mar 22 2011 Moebius transform is length 9 sequence [1, 0, 0, 0, 0, 0, 0, 0, -1]. - Michael Somos, Mar 22 2011 Expansion of x * (1 - x^8) / ((1 - x) * (1 - x^9)) in powers of x. - Michael Somos, Mar 22 2011 Multiplicative with a(p^e) = (if p=3 then 0^(e-1) else 1), p prime and e>0. a(n) = a(n+9) = a(-n) for all n in Z. a(n) = A000007(A010878(n)). a(A168183(n)) = 1. a(A008591(n)) = 0. A033441(n) = Sum_{k=0..n} a(k)*(n-k). 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 Dirichlet g.f. (1-3^(-2s))*zeta(s). - R. J. Mathar, Mar 06 2011 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 a(n) = 1 - A267142(n). - Antti Karttunen, Oct 07 2017 EXAMPLE 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 + ... MATHEMATICA A168182[n_]:=Boole[!Divisible[n, 9]]; Array[A168182, 10, 0] PROG (PARI) {a(n) = sign(n%9)}; /* Michael Somos, Mar 22 2011 */ CROSSREFS Cf. A168185, A145568, A168184, A168181, A109720, A097325, A011558, A166486, A011655, A000035, A267142, A033441. Sequence in context: A324732 A164980 A252372 * A204447 A188642 A168046 Adjacent sequences: A168179 A168180 A168181 * A168183 A168184 A168185 KEYWORD easy,mult,nonn AUTHOR Reinhard Zumkeller, Nov 30 2009 STATUS approved

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Last modified December 7 22:02 EST 2022. Contains 358671 sequences. (Running on oeis4.)