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A132740
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Largest divisor of n coprime to 10.
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15
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1, 1, 3, 1, 1, 3, 7, 1, 9, 1, 11, 3, 13, 7, 3, 1, 17, 9, 19, 1, 21, 11, 23, 3, 1, 13, 27, 7, 29, 3, 31, 1, 33, 17, 7, 9, 37, 19, 39, 1, 41, 21, 43, 11, 9, 23, 47, 3, 49, 1, 51, 13, 53, 27, 11, 7, 57, 29, 59, 3, 61, 31, 63, 1, 13, 33, 67, 17, 69, 7, 71, 9, 73, 37, 3, 19, 77, 39, 79, 1, 81
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OFFSET
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1,3
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COMMENTS
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Or: n with all factors of 2 and 5 removed. - M. F. Hasler, Apr 25 2017
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A000265(A132739(n)) = A132739(A000265(n)) = n / A132741(n);
A051626(a(n)) = A051626(n); A007732(a(n)) = A007732(n);
a(A003592(n)) = 1.
Multiplicative with a(2^e) = 1, a(5^e) = 1 and a(p^e) = p^e for p = 3 and p >= 7.
Dirichlet g.f. zeta(s-1)*(2^s-2)*(5^s-5)/((2^s-1)*(5^s-1)). - R. J. Mathar, Sep 06 2011
Sum_{k=1..n} a(k) ~ (5/18) * n^2. - Amiram Eldar, Nov 28 2022
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EXAMPLE
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a(1050) = a(2*3*5*5*7) = 3*7 = 21.
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MAPLE
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A132740 := proc(n) n/A132741(n) ; end proc: # R. J. Mathar, Sep 06 2011
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MATHEMATICA
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a[n_] := FixedPoint[ Quotient[#, GCD[#, 10]]& , n]; Table[a[n], {n, 1, 81}] (* Jean-François Alcover, Sep 06 2011, after Vladimir Joseph Stephan Orlovsky *)
Table[SelectFirst[Reverse[Divisors[n]], CoprimeQ[#, 10]&], {n, 90}] (* Uses the SelectFirst function from Mathematica version 10. - Harvey P. Dale, Mar 22 2015 *)
a[n_] := n / Times @@ ({2, 5}^IntegerExponent[n, {2, 5}]); Array[a, 100] (* Amiram Eldar, Jun 12 2022 *)
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PROG
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(Haskell) a132740 = a132739 . a000265 -- Reinhard Zumkeller, Apr 08 2011
(PARI) a(n)=n/5^valuation(n, 5)>>valuation(n, 2) \\ Charles R Greathouse IV, Sep 06 2011
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CROSSREFS
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Cf. A000265, A003592, A069105, A070021, A070022, A070023, A132739, A132741.
Sequence in context: A140211 A248101 A097706 * A106621 A011085 A199922
Adjacent sequences: A132737 A132738 A132739 * A132741 A132742 A132743
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KEYWORD
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nonn,mult,easy
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AUTHOR
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Reinhard Zumkeller, Aug 27 2007
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EXTENSIONS
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Edited by M. F. Hasler, Apr 25 2017
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STATUS
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approved
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