cp's OEIS Frontend

A145568 Characteristic function of numbers relatively prime to 11.

%I A145568 #26 Dec 12 2023 08:24:59
%S A145568 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,
%T A145568 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,
%U A145568 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
%N A145568 Characteristic function of numbers relatively prime to 11.
%C A145568 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.
%C A145568 Contribution from _Reinhard Zumkeller_, Nov 30 2009: (Start)
%C A145568 a(n)=A000007(A010880(n)); a(A160542(n))=1; a(A008593(n))=0;
%C A145568 A033443(n) = SUM(a(k)*(n-k): 0<=k<=n). (End)
%H A145568 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H A145568 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A145568 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F A145568 a(n)=1 if gcd(n,11)=1, else 0. Periodic with period 11: a(n+11)=a(11).
%F A145568 O.g.f.: x*sum(x^k,k=0..9)/(1-x^11).
%F A145568 Completely multiplicative with a(p) = (if p=11 then 0 else 1), p prime. [From _Reinhard Zumkeller_, Nov 30 2009]
%F A145568 Dirichlet g.f. (1-11^(-s))*zeta(s). - R. J. Mathar, Mar 06 2011
%F A145568 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
%t A145568 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 *)
%o A145568 (PARI) a(n)=gcd(n,11)==1 \\ _Charles R Greathouse IV_, Jun 28 2015
%Y A145568 A000035, A011655, A011558, A109720 for coprimality with 2,3,5,7, respectively.
%Y A145568 Cf. A168185, A168184, A168182, A168181, A097325, A166486.
%K A145568 nonn,mult,easy
%O A145568 0,1
%A A145568 _Wolfdieter Lang_ Feb 05 2009