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Positive integers k where d(d(k)) is coprime to k, where d(k) is the number of divisors of k.
3

%I #20 Sep 08 2022 08:45:35

%S 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,

%T 46,47,49,53,55,58,59,61,62,63,65,67,71,73,74,75,77,79,81,82,83,85,86,

%U 89,91,94,95,97,99,100,101,103,105,106,107,109,113,115,117,118,119,121

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

%C Includes all primes, squares of odd primes, and squarefree semiprimes coprime to 3. - _Robert Israel_, Dec 16 2019

%H Robert Israel, <a href="/A141114/b141114.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n) uses numtheory;

%p igcd(tau(tau(n)), n) = 1

%p end proc:

%p select(filter, [$1..200]); # _Robert Israel_, Dec 16 2019

%t Select[Range[200], GCD[DivisorSigma[0, DivisorSigma[0, # ]], # ] == 1 &] (* _Stefan Steinerberger_, Jun 05 2008 *)

%o (Magma) [k:k in [1..130]|Gcd(k,#Divisors(#Divisors(k))) eq 1]; // _Marius A. Burtea_, Dec 16 2019

%o (PARI) is(n) = gcd(numdiv(numdiv(n)), n)==1 \\ _Felix Fröhlich_, Dec 16 2019

%Y Cf. A010553, A141113, A141115.

%K nonn

%O 1,2

%A _Leroy Quet_, Jun 04 2008

%E More terms from _Stefan Steinerberger_, Jun 05 2008