A141114 Positive integers k where d(d(k)) is coprime to k, where d(k) is the number of divisors of k.

1, 3, 5, 7, 8, 9, 10, 11, 13, 14, 17, 19, 22, 23, 25, 26, 29, 31, 34, 35, 37, 38, 41, 43, 45, 46, 47, 49, 53, 55, 58, 59, 61, 62, 63, 65, 67, 71, 73, 74, 75, 77, 79, 81, 82, 83, 85, 86, 89, 91, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 113, 115, 117, 118, 119, 121

Offset: 1

Author

Leroy Quet, Jun 04 2008

Keywords

• nonn

Comments

Includes all primes, squares of odd primes, and squarefree semiprimes coprime to 3. - Robert Israel, Dec 16 2019

Examples

			26 has 4 divisors and 4 has 3 divisors. 3 is coprime to 26, so 26 is in the sequence.
		

Links

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

Crossrefs

Cf. A010553, A141113, A141115.

Programs

Magma

[k:k in [1..130]|Gcd(k,#Divisors(#Divisors(k))) eq 1]; // Marius A. Burtea, Dec 16 2019

Maple

filter:= proc(n) uses numtheory;
  igcd(tau(tau(n)), n) = 1
end proc:
select(filter, [$1..200]); # Robert Israel, Dec 16 2019

Mathematica

Select[Range[200], GCD[DivisorSigma[0, DivisorSigma[0, # ]], # ] == 1 &] (* Stefan Steinerberger, Jun 05 2008 *)

PARI

is(n) = gcd(numdiv(numdiv(n)), n)==1 \\ Felix Fröhlich, Dec 16 2019

Extensions

More terms from Stefan Steinerberger, Jun 05 2008