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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

Table of n, a(n) for n=0..104.

Michael Somos, Rational Function Multiplicative Coefficients

Index entries for characteristic functions

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(a(k)*(n-k): 0<=k<=n).

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

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.

Sequence in context: A079421 A168181 A164980 * A168046 A168184 A013595

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 May 25 12:08 EDT 2017. Contains 287027 sequences.