A145568 Characteristic function of numbers relatively prime to 11.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1

Offset

0,1

Comments

The x-powers appearing in the numerator polynomial of the o.g.f., given below, give the numbers from 0,1,...,10 which survive the sieve of Eratosthenes for multiples of 11, namely 1,2,...10.

Contribution from Reinhard Zumkeller, Nov 30 2009: (Start)

a(n)=A000007(A010880(n)); a(A160542(n))=1; a(A008593(n))=0;

A033443(n) = SUM(a(k)*(n-k): 0<=k<=n). (End)

Links

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

Index entries for characteristic functions

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Formula

a(n)=1 if gcd(n,11)=1, else 0. Periodic with period 11: a(n+11)=a(11).

O.g.f.: x*sum(x^k,k=0..9)/(1-x^11).

Completely multiplicative with a(p) = (if p=11 then 0 else 1), p prime. [From Reinhard Zumkeller, Nov 30 2009]

Dirichlet g.f. (1-11^(-s))*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

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 105] (* Ray Chandler, Aug 26 2015 *)

Prog

(PARI) a(n)=gcd(n, 11)==1 \\ Charles R Greathouse IV, Jun 28 2015

Crossrefs

A000035, A011655, A011558, A109720 for coprimality with 2,3,5,7, respectively.

Cf. A168185, A168184, A168182, A168181, A097325, A166486.

Sequence in context: A360122 A369006 A011582 * A168185 A011583 A011584

Adjacent sequences: A145565 A145566 A145567 * A145569 A145570 A145571

Keyword

nonn,mult,easy

Author

Wolfdieter Lang Feb 05 2009

Status

approved