login
A141114
Positive integers k where d(d(k)) is coprime to k, where d(k) is the number of divisors of k.
3
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
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Jun 04 2008
EXTENSIONS
More terms from Stefan Steinerberger, Jun 05 2008
STATUS
approved