A091684 a(n) = 0 if n is divisible by 3, otherwise a(n) = n.

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, 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, 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

Offset: 0

Author

Paul Barry, Jan 28 2004

Keywords

• nonn
• mult
• easy

Comments

Multiplicative with a(3^e) = 0, a(p^e) = p^e otherwise. - Mitch Harris, Jun 09 2005

Completely multiplicative with a(3) = 0, a(p) = p otherwise. - Charles R Greathouse IV, Feb 21 2011

Examples

			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 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index to divisibility sequences
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A008585, A100050.

Programs

Magma

&cat[[0,3*n+1,3*n+2]: n in [0..26]];  // Bruno Berselli, Aug 29 2011

Mathematica

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 *)
{#,0,#}[[Mod[#-1,3,1]]]&/@Range[0,99] (* Federico Provvedi, Jun 15 2021 *)

PARI

a(n)=if(n%3,n) \\ Charles R Greathouse IV, Feb 21 2011

PARI

{a(n) = n * sign( n%3)} /* Michael Somos, Mar 19 2011 */

Formula

a(n) = Product_{k=0..2} Sum_{j=1..n} w(3)^(k*j), w(3)=e^(2*Pi*i/3), i=sqrt(-1).

a(n) = 2*n/3 - n*sin(2*Pi*n/3 + Pi/3)/sqrt(3) - n*cos(2*Pi*n/3 + Pi/3)/3.

G.f.: x*(x^4 + 2*x^3 + 2*x + 1)/((x^2 + x + 1)^2*(x - 1)^2). - Ralf Stephan, Jan 29 2004

a(n) = n^3 mod 3n = A000027(n)*A011655(n). - Paul Barry, Apr 13 2005

Dirichlet g.f.: zeta(s-1)*(1-1/3^(s-1)). - R. J. Mathar, Feb 10 2011

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

a(n) = n * sign(n mod 3). - Wesley Ivan Hurt, Sep 24 2017