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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
OFFSET
1,3
COMMENTS
Apparently also the denominator of A007955(n)/A000005(n). See A291186. - Jaroslav Krizek, Sep 05 2017
LINKS
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))); forstep(k=#d, 1, -1, if (gcd(d[k], n) == 1, return (d[k]))); \\ Michel Marcus, Sep 22 2017; corrected Jun 13 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 23 2008
EXTENSIONS
More terms from Stefan Steinerberger, Mar 09 2008
STATUS
approved