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 A051176 If n mod 3 = 0 then n/3 else n. 33
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Multiplicative with a(3^e) = 3^(e-1), a(p^e) = p^e otherwise. - Mitch Harris, Jun 09 2005 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 a(n) = A167192(n+3, 3). - Reinhard Zumkeller, Oct 30 2009 a(n) = A109044(n)/3. Dirichlet g.f. zeta(s-1)*(1-2/3^s). - R. J. Mathar, Apr 18 2011 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 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). Sequence in context: A106610 A182398 A214736 * A145064 A209166 A209146 Adjacent sequences:  A051173 A051174 A051175 * A051177 A051178 A051179 KEYWORD nonn,easy,mult AUTHOR STATUS approved

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Last modified May 23 11:05 EDT 2019. Contains 323513 sequences. (Running on oeis4.)