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

1,3

Comments

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

Links

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

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

Crossrefs

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

Keyword

nonn,mult,easy

Author

Reinhard Zumkeller, Aug 27 2007

Extensions

Edited by M. F. Hasler, Apr 25 2017

Status

approved