A132740 Largest divisor of n coprime to 10.

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

Author

Reinhard Zumkeller, Aug 27 2007

Keywords

• nonn
• mult
• easy

Comments

Or: n with all factors of 2 and 5 removed. - M. F. Hasler, Apr 25 2017

Examples

			a(1050) = a(2*3*5*5*7) = 3*7 = 21.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000265, A003592, A069105, A070021, A070022, A070023, A132739, A132741.

Programs

Haskell

a132740 = a132739 . a000265  -- Reinhard Zumkeller, Apr 08 2011

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 *)

PARI

a(n)=n/5^valuation(n,5)>>valuation(n,2) \\ Charles R Greathouse IV, Sep 06 2011

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

Extensions

Edited by M. F. Hasler, Apr 25 2017