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A065330
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a(n) = Max { k | gcd(n, k) = k and gcd(k, 6) = 1 }.
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10
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1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 5, 1, 17, 1, 19, 5, 7, 11, 23, 1, 25, 13, 1, 7, 29, 5, 31, 1, 11, 17, 35, 1, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 1, 49, 25, 17, 13, 53, 1, 55, 7, 19, 29, 59, 5, 61, 31, 7, 1, 65, 11, 67, 17, 23, 35, 71, 1, 73, 37, 25, 19, 77, 13, 79, 5, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| a(n) * A065331(n) = n.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| Multiplicative with a(2^e)=1, a(3^e)=1, a(p^e)=p^e, p>3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 02 2001
A106799(n) = A001222(a(n)). - Reinhard Zumkeller, May 19 2005
a(1)=1; then a(2n)=a(n), a(2n+1)=a((2n+1)/3) if 2n+1 is divisible by 3, a(2n+1)=2n+1 otherwise - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 04 2007
Dirichlet g.f. zeta(s-1)*(1-2^(1-s))*(1-3^(1-s))/ ( (1-2^(-s))*(1-3^(-s)) ). - R. J. Mathar, Jul 04 2011
a(n) = A038502(A000265(n)). [Reinhard Zumkeller, Jul 6 2011]
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EXAMPLE
| a(30) = 5.
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MATHEMATICA
| f[n_] := Times @@ (First@#^Last@# & /@ Select[FactorInteger@n, First@# != 2 && First@# != 3 &]); Array[f, 81] (* Robert G. Wilson v Aug 18 2006 *)
f[n_]:=Denominator[6^n/n]; Array[f, 100] (*From Vladimir Joseph Stephan Orlovsky, Feb 16 2011*)
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PROG
| (PARI) a(n)=if(n<2, 1, if(n%2, if(n%3, n, a(n/3)), a(n/2))) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 04 2007
(Haskell)
a065330 = a038502 . a000265 -- Reinhard Zumkeller, Jul 6 2011
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CROSSREFS
| A065331
Cf. A000265, A038502.
Sequence in context: A052345 A197733 A111008 * A140215 A190643 A068328
Adjacent sequences: A065327 A065328 A065329 * A065331 A065332 A065333
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KEYWORD
| mult,nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 29 2001
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