Search: id:A063524
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%I A063524
%S A063524 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,
%T A063524 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,
%U A063524 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
%N A063524 Characteristic function of 1.
%C A063524 The identity function for Dirichlet multiplication (see Apostol).
%C A063524 Sum of the Moebius function mu(d) of the divisors d of n. - Robert G. 
               Wilson v (rgwv(AT)rgwv.com), Sep 30 2006
%C A063524 -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.
%C A063524 a(A000012(n)) = 1; a(A087156(n)) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 11 2008]
%C A063524 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]
%D A063524 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 
               1976, page 30.
%H A063524 G. P. Michon, <a href="http://www.numericana.com/answer/numbers.htm#multiplicative">
               Multiplicative Functions</a>.
%H A063524 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A063524 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%F A063524 a(n)=(n!^2 mod (n+1))*((n+1)!^2 mod (n+2)), with n>=0 - Paolo P. Lava 
               (ppl(AT)spl.at), Apr 24 2007
%F A063524 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 (ppl(AT)spl.at), Aug 31 2007
%F A063524 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 (ppl(AT)spl.at), Aug 31 2007
%F A063524 G.f.: x . E.g.f.: x . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 25 2008]
%F A063524 a(n)=mu(n^2) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Sep 
               04 2009]
%F A063524 a(n)=floor(n/A000203(n)) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), 
               Nov 11 2009]
%p A063524 A063524 := proc(n) if n = 1 then 1 else 0; fi; end;
%t A063524 Table[If[n == 1, 1, 0], {n, 0, 104}] (* Robert G. Wilson v Sep 30 2006 
               *)
%Y A063524 Cf. A000007.
%Y A063524 Cf. A008683, A000012, A007427, A000005, A007428, A007425. [From Jaroslav 
               Krizek (jaroslav.krizek(AT)atlas.cz), Mar 03 2009]
%Y A063524 Sequence in context: A104121 A157928 A159075 this_sequence A084928 A033683 
               A130638
%Y A063524 Adjacent sequences: A063521 A063522 A063523 this_sequence A063525 A063526 
               A063527
%K A063524 easy,nonn,mult,new
%O A063524 0,1
%A A063524 Labos E. (labos(AT)ana.sote.hu), Jul 30 2001

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