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URL: https://oeis.org/A132740

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A132740
Largest divisor of n coprime to 10.
18
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
OFFSET
1,3
COMMENTS
Or: n with all factors of 2 and 5 removed. - M. F. Hasler, Apr 25 2017
LINKS
FORMULA
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
EXAMPLE
a(1050) = a(2*3*5*5*7) = 3*7 = 21.
MAPLE
A132740 := proc(n) n/A132741(n) ; end proc: # R. J. Mathar, Sep 06 2011
MATHEMATICA
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 *)
PROG
(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
KEYWORD
nonn,mult,easy
AUTHOR
Reinhard Zumkeller, Aug 27 2007
EXTENSIONS
Edited by M. F. Hasler, Apr 25 2017
STATUS
approved