A051176 If n mod 3 = 0 then n/3 else n.

0, 1, 2, 1, 4, 5, 2, 7, 8, 3, 10, 11, 4, 13, 14, 5, 16, 17, 6, 19, 20, 7, 22, 23, 8, 25, 26, 9, 28, 29, 10, 31, 32, 11, 34, 35, 12, 37, 38, 13, 40, 41, 14, 43, 44, 15, 46, 47, 16, 49, 50, 17, 52, 53, 18, 55, 56, 19, 58, 59, 20, 61, 62, 21, 64, 65, 22, 67

Offset

0,3

Comments

Numerator of n/3. - Wesley Ivan Hurt, Jul 18 2014

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Formula

a(n) = n / gcd(n,3).

G.f.: x*(1+2*x+x^2+2*x^3+x^4)/(1-x^3)^2 = x*(1+2*x+x^2+2*x^3+x^4) / ( (x-1)^2*(1+x+x^2)^2 ). - Len Smiley, Apr 30 2001

Multiplicative with a(3^e) = 3^(e-1), a(p^e) = p^e otherwise. - Mitch Harris, Jun 09 2005

a(n) = A167192(n+3, 3). - Reinhard Zumkeller, Oct 30 2009

From R. J. Mathar, Apr 18 2011: (Start)

a(n) = A109044(n)/3.

Dirichlet g.f.: zeta(s-1)*(1-2/3^s). (End)

a(n) = n/3 * (1 + 2*A011655(n)) = n*A144437(n)/3. - Timothy Hopper, Feb 23 2017

G.f.: x /(1 - x)^2 - 2 * x^3/(1 - x^3)^2. - Michael Somos, Mar 05 2017

a(n) = a(-n) for all n in Z. - Michael Somos, Mar 05 2017

a(n) = n*(7 - 4*cos((2*Pi*n)/3)) / 9. - Colin Barker, Mar 05 2017

Sum_{k=1..n} a(k) ~ (7/18) * n^2. - Amiram Eldar, Nov 25 2022

Sum_{n>=1} (-1)^(n+1)/a(n) = 5*log(2)/3. - Amiram Eldar, Sep 08 2023

Example

G.f. = x + 2*x^2 + x^3 + 4*x^4 + 5*x^5 + 2*x^6 + 7*x^7 + 8*x^8 + 3*x^9 + ...

Maple

A051176:=n->numer(n/3); seq(A051176(n), n=0..100); # Wesley Ivan Hurt, Jul 18 2014

Mathematica

If[Divisible[#, 3], #/3, #]&/@Range[0, 70] (* Harvey P. Dale, Feb 07 2011 *)
a[n_] := Numerator[n/3]; Array[a, 100, 0] (* Wesley Ivan Hurt, Jul 18 2014 *)

Prog

(Haskell)
a051176 n = if m == 0 then n' else n  where (n', m) = divMod n 3
-- Reinhard Zumkeller, Aug 27 2012
(PARI) a(n) = if (n % 3, n, n/3); \\ Michel Marcus, Feb 02 2016
(Magma) [Numerator(n/3): n in [0..70]]; // G. C. Greubel, Feb 19 2019
(Sage) [numerator(n/3) for n in range(70)] # G. C. Greubel, Feb 19 2019

Crossrefs

Cf. A026741, A051176, A060819, A060791, A060789 for n / GCD(n,k) for k=2..6. See also A106608 thru A106612 (k = 7 thru 11), A051724 (k = 12), A106614 thru A106621 (k = 13 thru 20).

Cf. A109044, A011655, A144437, A167192.

Sequence in context: A106610 A182398 A214736 * A145064 A209166 A209146

Adjacent sequences: A051173 A051174 A051175 * A051177 A051178 A051179

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved