A137926 a(n) = the largest divisor of n that is coprime to A000005(n). (A000005(n) = the number of positive divisors of n.)

1, 1, 3, 4, 5, 3, 7, 1, 1, 5, 11, 1, 13, 7, 15, 16, 17, 1, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 1, 33, 17, 35, 4, 37, 19, 39, 5, 41, 21, 43, 11, 5, 23, 47, 3, 49, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 5, 61, 31, 7, 64, 65, 33, 67, 17, 69, 35, 71, 1, 73, 37, 25, 19, 77, 39, 79

Offset: 1

Author

Leroy Quet, Feb 23 2008

Keywords

• nonn

Examples

			6 has 4 positive divisors. The divisors of 6 are 1,2,3,6. The divisors of 6 that are coprime to 4 are 1 and 3. 3 is the largest of these; so a(6) = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046642 (a(n)=n), A120737 (a(n)=1), A137927.

Programs

Maple

f := proc (n) local D, t; D := numtheory:-divisors(n); t := nops(D); max(select(proc (d) options operator, arrow; igcd(d, t) = 1 end proc, D)) end proc:
map(f, [$1..100]); # Robert Israel, Feb 11 2018

Mathematica

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

PARI

a(n) = {my(d = divisors(n)); vecmax(select(x->(gcd(x, #d) == 1), d));} \\ Michel Marcus, Feb 12 2018

Extensions

More terms from Stefan Steinerberger, Mar 09 2008