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A051176
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If n mod 3 = 0 then n/3 else n.
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35
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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
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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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
Dirichlet g.f.: zeta(s-1)*(1-2/3^s). (End)
G.f.: x /(1 - x)^2 - 2 * x^3/(1 - x^3)^2. - 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
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EXAMPLE
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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 + ...
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MAPLE
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MATHEMATICA
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If[Divisible[#, 3], #/3, #]&/@Range[0, 70] (* Harvey P. Dale, Feb 07 2011 *)
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PROG
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(Haskell)
a051176 n = if m == 0 then n' else n where (n', m) = divMod n 3
(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
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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