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

Author

Wolfdieter Lang Feb 05 2009

Keywords

• nonn
• mult
• easy

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

• 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).

Crossrefs

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

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

Programs

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 *)

PARI

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

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