A137927 a(n) = the largest divisor of A000005(n) that is coprime to n. (A000005(n) = the number of positive divisors of n.).

1, 1, 2, 3, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 4, 5, 2, 1, 2, 3, 4, 1, 2, 1, 3, 1, 4, 3, 2, 1, 2, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 1, 2, 3, 2, 1, 2, 5, 3, 3, 4, 3, 2, 1, 4, 1, 4, 1, 2, 1, 2, 1, 2, 7, 4, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 1

Offset: 1

Author

Leroy Quet, Feb 23 2008

Keywords

• nonn

Comments

Apparently also the denominator of A007955(n)/A000005(n). See A291186. - Jaroslav Krizek, Sep 05 2017

Examples

			20 has 6 positive divisors. The divisors of 6 are 1,2,3,6. The divisors of 6 that are coprime to 20 are 1 and 3. 3 is the largest of these; so a(20) = 3.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A137926, A007955, A120736, A291899.

Programs

Maple

A137927 := proc(n)
    local a;
    a := 1 ;
    for d in numtheory[divisors](numtheory[tau](n)) do
        if igcd(d,n) = 1 then
            a := max(a,d) ;
        end if:
    end do:
    a ;
end proc:
seq(A137927(n),n=1..100) ; # R. J. Mathar, Sep 22 2017

Mathematica

Table[Select[Divisors[Length[Divisors[n]]], GCD[ #, n] == 1 &][[ -1]], {n, 1, 80}] (* Stefan Steinerberger, Mar 09 2008 *)

PARI

a(n) = my(d=divisors(numdiv(n))); forstep(k=#d, 1, -1, if (gcd(d[k], n) == 1, return (d[k]))); \\ Michel Marcus, Sep 22 2017; corrected Jun 13 2022

Extensions

More terms from Stefan Steinerberger, Mar 09 2008