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A145568
Characteristic function of numbers relatively prime to 11.
10
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)
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.
Sequence in context: A360122 A369006 A011582 * A168185 A011583 A011584
KEYWORD
nonn,mult,easy
AUTHOR
Wolfdieter Lang Feb 05 2009
STATUS
approved