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A063524
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Characteristic function of 1.
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47
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0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The identity function for Dirichlet multiplication (see Apostol).
Sum of the Moebius function mu(d) of the divisors d of n. - Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 30 2006
-a(n) is the Hankel transform of A000045(n),n>=0 (Fibonacci numbers). See A055879 for the definition of Hankel transform. W. Lang Jan 23 2007.
a(A000012(n)) = 1; a(A087156(n)) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 11 2008]
a(n) for n >= 1 is Dirichlet convolution of following functions b(n), c(n), a(n) = Sum_{d|n} b(d)*c(n/d)): a(n) = A008683(n) * A000012(n), a(n) = A007427(n) * A000005(n), a(n) = A007428(n) * A007425(n). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 03 2009]
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REFERENCES
| T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 30.
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LINKS
| G. P. Michon, Multiplicative Functions.
Index entries for sequences related to linear recurrences with constant coefficients
Index entries for characteristic functions
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FORMULA
| a(n)=(n!^2 mod (n+1))*((n+1)!^2 mod (n+2)), with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Apr 24 2007
a(n) = C((n+1)^2,n+3) mod 2 = C((n+13)^4,n+15) mod 2 = C((n+61)^6,n+63) mod 2 etc. - Paolo P. Lava (paoloplava(AT)gmail.com), Aug 31 2007
Any sequence formed from zeros and a unique 1 can be produced using the formula a(n) = C(n^2k,n+2) mod 2, where k is a positive integer and n>=0. The sequence is formed by [2^2k-2 initial zeros] U [1] U [infinitely many zeros]. If we want to have 1 in a specific position the formula must be modified: a(n) = C((n+m)^2k,n+2+m) mod 2, where k and m are positive integers and n>=0. In this way we have {2^2k-2-m initial zeros} U {1} U {infinitely many zeros}. Of course we must have 2^2k-2>m. Then if we want the unique 1 in the position r, the minimum power k we can use is given by the relation 2^2k-1 >= r, namely k>=(1/2)*Log_2 (r+1). - Paolo P. Lava (paoloplava(AT)gmail.com), Aug 31 2007
G.f.: x . E.g.f.: x . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 25 2008]
a(n)=mu(n^2) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Sep 04 2009]
a(n)=floor(n/A000203(n)) for n>0. [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Nov 11 2009]
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MAPLE
| A063524 := proc(n) if n = 1 then 1 else 0; fi; end;
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MATHEMATICA
| Table[If[n == 1, 1, 0], {n, 0, 104}] (* Robert G. Wilson v Sep 30 2006 *)
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CROSSREFS
| Cf. A000007.
Cf. A008683, A000012, A007427, A000005, A007428, A007425. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 03 2009]
Sequence in context: A157928 A159075 A178333 * A084928 A033683 A130638
Adjacent sequences: A063521 A063522 A063523 * A063525 A063526 A063527
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KEYWORD
| easy,nonn,mult
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 30 2001
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