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A137927 a(n) = the largest divisor of A000005(n) that is coprime to n. (A000005(n) = the number of positive divisors of n.). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

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

EXAMPLE

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.

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 *)

PROG

(PARI) a(n) = my(d=divisors(numdiv(n))); vecmax(select(x->(x==1), vector(#d, k, gcd(k, n)), 1)); \\ Michel Marcus, Sep 22 2017

CROSSREFS

Cf. A137926, A007955, A120736, A291899.

Sequence in context: A316657 A277914 A126626 * A321864 A084311 A026490

Adjacent sequences:  A137924 A137925 A137926 * A137928 A137929 A137930

KEYWORD

nonn

AUTHOR

Leroy Quet, Feb 23 2008

EXTENSIONS

More terms from Stefan Steinerberger, Mar 09 2008

STATUS

approved

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Last modified March 20 16:16 EDT 2019. Contains 321345 sequences. (Running on oeis4.)