A126773 a(n) = largest divisor of n which is coprime to the largest proper divisor of n. (a(1)=1.).

1, 2, 3, 1, 5, 2, 7, 1, 1, 2, 11, 1, 13, 2, 3, 1, 17, 2, 19, 1, 3, 2, 23, 1, 1, 2, 1, 1, 29, 2, 31, 1, 3, 2, 5, 1, 37, 2, 3, 1, 41, 2, 43, 1, 1, 2, 47, 1, 1, 2, 3, 1, 53, 2, 5, 1, 3, 2, 59, 1, 61, 2, 1, 1, 5, 2, 67, 1, 3, 2, 71, 1, 73, 2, 3, 1, 7, 2, 79, 1, 1, 2, 83, 1, 5, 2, 3, 1, 89, 2, 7, 1, 3, 2, 5, 1

Offset: 1

Author

Leroy Quet, Feb 17 2007

Keywords

• nonn

Comments

Also the denominator of the ratio of the largest proper divisor to the least prime divisor of n, which can be thought of as the ratio of the 2nd largest divisor to the 2nd least divisor of n. - Michel Marcus, Feb 27 2017

Examples

			The largest proper divisor of 30 is A032742(30) = 15. So a(30)= 2, because 2 is the largest divisor of 30 which is coprime to 15.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Maple

A126773 := proc(n)
    local p ;
    p := A020639(n) ;
    if modp(n,p^2) = 0 then
        1 ;
    else
        p ;
    end if;
end proc:
seq(A126773(n),n=1..100) ; # R. J. Mathar, Mar 03 2017

Mathematica

f[n_] := Block[{d = Divisors[n]},If[n < 2, 1, Max @@ Select[d, GCD[ #, d[[ -2]]] == 1 &]]];Array[f, 100] (* Ray Chandler, Feb 26 2007 *)

PARI

a(n) = if (n==1, 1, my(d = divisors(n)); k = #d; while (gcd(d[k], d[#d-1]) != 1, k--); d[k]); \\ Michel Marcus, Feb 27 2017

PARI

a(n) = if (n==1, 1, my(d = divisors(n)); denominator(d[#d-1]/d[2])); \\ Michel Marcus, Feb 27 2017

PARI

a(n)=if(n==1, return(1)); my(f=factor(n)[1,]); if(f[2]>1, 1, f[1]) \\ Charles R Greathouse IV, Feb 27 2017

Formula

For n >= 2: Let p =A020639(n) be the smallest prime dividing n. If p^2 divides n, then a(n)=1. Otherwise, a(n) = p.

Extensions

Extended by Ray Chandler, Feb 26 2007