A168182 Characteristic function of numbers that are not multiples of 9.

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

Links

Antti Karttunen, Table of n, a(n) for n = 0..999

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_{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 A368905 A188642

Adjacent sequences: A168179 A168180 A168181 * A168183 A168184 A168185

Keyword

easy,mult,nonn

Author

Reinhard Zumkeller, Nov 30 2009

Status

approved