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A065331
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Largest 3-smooth divisor of n.
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27
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1, 2, 3, 4, 1, 6, 1, 8, 9, 2, 1, 12, 1, 2, 3, 16, 1, 18, 1, 4, 3, 2, 1, 24, 1, 2, 27, 4, 1, 6, 1, 32, 3, 2, 1, 36, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 48, 1, 2, 3, 4, 1, 54, 1, 8, 3, 2, 1, 12, 1, 2, 9, 64, 1, 6, 1, 4, 3, 2, 1, 72, 1, 2, 3, 4, 1, 6, 1, 16, 81, 2, 1, 12, 1, 2, 3, 8, 1, 18, 1, 4, 3, 2, 1, 96
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Multiplicative with a(2^e)=2^e, a(3^e)=3^e, a(p^e)=1, p>3. - Vladeta Jovovic, Nov 05 2001
Dirichlet g.f.: zeta(s)*(1-2^(-s))*(1-3^(-s))/ ( (1-2^(1-s))*(1-3^(1-s)) ). - R. J. Mathar, Jul 04 2011
Sum_{k=1..n} a(k) ~ n*(log(n)^2 + (2*gamma + 3*log(2) + 2*log(3) - 2)*log(n) + (2 + log(2)^2/6 + 3*log(2)*(log(3) - 1) - 2*log(3) + log(3)^2/6 + gamma*(3*log(2) + 2*log(3) - 2) - 2*sg1)) / (6*log(2)*log(3)), where gamma is the Euler-Mascheroni constant A001620 and sg1 is the first Stieltjes constant (see A082633). - Vaclav Kotesovec, Sep 19 2020
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MAPLE
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seq(2^padic:-ordp(n, 2)*3^padic:-ordp(n, 3), n=1..100); # Robert Israel, Feb 08 2016
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MATHEMATICA
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a[n_] := Times @@ ({2, 3}^IntegerExponent[n, {2, 3}]); Array[a, 100] (* Amiram Eldar, Sep 19 2020 *)
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PROG
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(PARI) a(n)=gcd(n, 6^n) \\ Not very efficient, but simple. Stanislav Sykora, Feb 08 2016
(Haskell)
a065331 = f 2 1 where
f p y x | r == 0 = f p (y * p) x'
| otherwise = if p == 2 then f 3 y x else y
where (x', r) = divMod x p
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CROSSREFS
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KEYWORD
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mult,nonn,easy
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AUTHOR
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STATUS
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approved
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