|
%I #46 Nov 28 2022 08:12:03
%S 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,
%T 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,
%U 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
%N Largest divisor of n coprime to 10.
%C Or: n with all factors of 2 and 5 removed. - _M. F. Hasler_, Apr 25 2017
%H Reinhard Zumkeller, <a href="/A132740/b132740.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000265(A132739(n)) = A132739(A000265(n)) = n / A132741(n);
%F A051626(a(n)) = A051626(n); A007732(a(n)) = A007732(n);
%F a(A003592(n)) = 1.
%F Multiplicative with a(2^e) = 1, a(5^e) = 1 and a(p^e) = p^e for p = 3 and p >= 7.
%F Dirichlet g.f. zeta(s-1)*(2^s-2)*(5^s-5)/((2^s-1)*(5^s-1)). - _R. J. Mathar_, Sep 06 2011
%F Sum_{k=1..n} a(k) ~ (5/18) * n^2. - _Amiram Eldar_, Nov 28 2022
%e a(1050) = a(2*3*5*5*7) = 3*7 = 21.
%p A132740 := proc(n) n/A132741(n) ; end proc: # _R. J. Mathar_, Sep 06 2011
%t a[n_] := FixedPoint[ Quotient[#, GCD[#, 10]]& , n]; Table[a[n], {n, 1, 81}] (* _Jean-François Alcover_, Sep 06 2011, after _Vladimir Joseph Stephan Orlovsky_ *)
%t Table[SelectFirst[Reverse[Divisors[n]],CoprimeQ[#,10]&],{n,90}] (* Uses the SelectFirst function from Mathematica version 10. - _Harvey P. Dale_, Mar 22 2015 *)
%t a[n_] := n / Times @@ ({2, 5}^IntegerExponent[n, {2, 5}]); Array[a, 100] (* _Amiram Eldar_, Jun 12 2022 *)
%o (Haskell) a132740 = a132739 . a000265 -- _Reinhard Zumkeller_, Apr 08 2011
%o (PARI) a(n)=n/5^valuation(n,5)>>valuation(n,2) \\ _Charles R Greathouse IV_, Sep 06 2011
%Y Cf. A000265, A003592, A069105, A070021, A070022, A070023, A132739, A132741.
%K nonn,mult,easy
%O 1,3
%A _Reinhard Zumkeller_, Aug 27 2007
%E Edited by _M. F. Hasler_, Apr 25 2017
|
