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%I #62 Sep 08 2022 08:45:13
%S 0,1,2,0,4,5,0,7,8,0,10,11,0,13,14,0,16,17,0,19,20,0,22,23,0,25,26,0,
%T 28,29,0,31,32,0,34,35,0,37,38,0,40,41,0,43,44,0,46,47,0,49,50,0,52,
%U 53,0,55,56,0,58,59,0,61,62,0,64,65,0,67,68,0,70,71,0,73,74,0,76,77,0,79,80
%N a(n) = 0 if n is divisible by 3, otherwise a(n) = n.
%C Multiplicative with a(3^e) = 0, a(p^e) = p^e otherwise. - _Mitch Harris_, Jun 09 2005
%C Completely multiplicative with a(3) = 0, a(p) = p otherwise. - _Charles R Greathouse IV_, Feb 21 2011
%H Vincenzo Librandi, <a href="/A091684/b091684.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F a(n) = Product_{k=0..2} Sum_{j=1..n} w(3)^(k*j), w(3)=e^(2*Pi*i/3), i=sqrt(-1).
%F a(n) = 2*n/3 - n*sin(2*Pi*n/3 + Pi/3)/sqrt(3) - n*cos(2*Pi*n/3 + Pi/3)/3.
%F G.f.: x*(x^4 + 2*x^3 + 2*x + 1)/((x^2 + x + 1)^2*(x - 1)^2). - _Ralf Stephan_, Jan 29 2004
%F a(n) = n^3 mod 3n. - _Paul Barry_, Apr 13 2005
%F Dirichlet g.f.: zeta(s-1)*(1-1/3^(s-1)). - _R. J. Mathar_, Feb 10 2011
%F a(3*n) = 0, a(3*n + 1) = 3*n + 1, a(3*n + 2) = 3*n + 2. a(-n) = -a(n). - _Michael Somos_, Mar 19 2011
%F a(n) = n * sign(n mod 3). - _Wesley Ivan Hurt_, Sep 24 2017
%e x + 2*x^2 + 4*x^4 + 5*x^5 + 7*x^7 + 8*x^8 + 10*x^10 + 11*x^11 + 13*x^13 + ...
%t f[n_] := If[ Mod[n, 3] == 0, 0, n] (* Or *) n (Fibonacci[n] - 2 Floor[ Fibonacci[n]/2]); Array[f, 78, 0] (* _Robert G. Wilson v_ *)
%t {#,0,#}[[Mod[#-1,3,1]]]&/@Range[0,99] (* _Federico Provvedi_, Jun 15 2021 *)
%o (PARI) a(n)=if(n%3,n) \\ _Charles R Greathouse IV_, Feb 21 2011
%o (PARI) {a(n) = n * sign( n%3)} /* _Michael Somos_, Mar 19 2011 */
%o (Magma) &cat[[0,3*n+1,3*n+2]: n in [0..26]]; // _Bruno Berselli_, Aug 29 2011
%Y Cf. A008585, A100050.
%K nonn,mult,easy
%O 0,3
%A _Paul Barry_, Jan 28 2004
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