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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
OFFSET
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 */
KEYWORD
easy,mult,nonn
AUTHOR
Reinhard Zumkeller, Nov 30 2009
STATUS
approved