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

1,2

Comments

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

Links

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

Example

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

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 *)

Prog

(Magma) [k:k in [1..130]|Gcd(k, #Divisors(#Divisors(k))) eq 1]; // Marius A. Burtea, Dec 16 2019
(PARI) is(n) = gcd(numdiv(numdiv(n)), n)==1 \\ Felix Fröhlich, Dec 16 2019

Crossrefs

Cf. A010553, A141113, A141115.

Sequence in context: A100318 A167707 A131903 * A136443 A247459 A020491

Adjacent sequences: A141111 A141112 A141113 * A141115 A141116 A141117

Keyword

nonn

Author

Leroy Quet, Jun 04 2008

Extensions

More terms from Stefan Steinerberger, Jun 05 2008

Status

approved