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A145568
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Characteristic function of numbers relatively prime to 11.
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10
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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 (reinhard.zumkeller(AT)gmail.com), 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)
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LINKS
| Index entries for characteristic functions [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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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).
a(n)=(n^10 mod 11), with n>=0. a(n)=(1/121)*{13*(n mod 11)+2*[(n+1) mod 11]+2*[(n+2) mod 11]+2*[(n+3) mod 11]+2*[(n+4) mod 11]+2*[(n+5) mod 11]+2*[(n+6) mod 11]+2*[(n+7) mod 11]+2*[(n+8) mod 11]+2*[(n+9) mod 11]-9*[(n+10) mod 11]}, with n>=0. [From Paolo P. Lava (paoloplava(AT)gmail.com), Feb 06 2009]
Completely multiplicative with a(p) = (if p=11 then 0 else 1), p prime. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
Dirichlet g.f. (1-11^(-s))*zeta(s). - R. J. Mathar, Mar 06 2011
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CROSSREFS
| A000035, A011655, A011558, A109720 for coprimality with 2,3,5,7, respectively.
Cf. A168185, A168184, A168182, A168181, A097325, A166486. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
Sequence in context: A168184 A013595 A011582 * A123927 A168185 A011583
Adjacent sequences: A145565 A145566 A145567 * A145569 A145570 A145571
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KEYWORD
| nonn,mult,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Feb 05 2009
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