A152443 a(n) = the largest proper divisor of n that is coprime to d(n), where d(n) = the number of divisors of n.

1, 1, 2, 1, 3, 1, 1, 1, 5, 1, 1, 1, 7, 5, 8, 1, 1, 1, 5, 7, 11, 1, 3, 5, 13, 9, 7, 1, 15, 1, 1, 11, 17, 7, 4, 1, 19, 13, 5, 1, 21, 1, 11, 5, 23, 1, 3, 7, 25, 17, 13, 1, 27, 11, 7, 19, 29, 1, 5, 1, 31, 7, 32, 13, 33, 1, 17, 23, 35, 1, 1, 1, 37, 25, 19, 11, 39, 1, 1, 27, 41, 1, 7, 17, 43, 29, 11, 1, 5

Offset: 2

Author

Leroy Quet, Dec 04 2008

Keywords

• nonn
• look

Comments

If n is squarefree then a(n) = A032742(n). - Robert Israel, Jun 23 2025

Examples

			There are 4 divisors of 27. These are 1,3,9,27. The proper divisors of 27 are therefore 1,3,9. The largest of these that is coprime to d(27) = 4 is 9. So a(27) = 9. (Note that in this case, the largest divisor of 27 coprime to 4 is 27, not 9.)
		

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A000005, A032742, A137926, A152444.

Programs

Maple

f:= proc(n) local d,D;
   D:= numtheory:-divisors(n);
   d:= nops(D);
   max(select(t -> igcd(d,t)=1, D minus {n}))
end proc:
map(f, [$2..100]); # Robert Israel, Jun 23 2025

Mathematica

Table[Max[Select[Drop[Divisors[n], -1], GCD[DivisorSigma[0, n], # ] == 1 &]], {n, 2, 100}] (* Stefan Steinerberger, Dec 06 2008 *)

Extensions

Extended by Ray Chandler and Stefan Steinerberger, Dec 05 2008