cp's OEIS Frontend

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

%I A141114 #20 Sep 08 2022 08:45:35
%S A141114 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 A141114 46,47,49,53,55,58,59,61,62,63,65,67,71,73,74,75,77,79,81,82,83,85,86,
%U A141114 89,91,94,95,97,99,100,101,103,105,106,107,109,113,115,117,118,119,121
%N A141114 Positive integers k where d(d(k)) is coprime to k, where d(k) is the number of divisors of k.
%C A141114 Includes all primes, squares of odd primes, and squarefree semiprimes coprime to 3. - _Robert Israel_, Dec 16 2019
%H A141114 Robert Israel, <a href="/A141114/b141114.txt">Table of n, a(n) for n = 1..10000</a>
%e A141114 26 has 4 divisors and 4 has 3 divisors. 3 is coprime to 26, so 26 is in the sequence.
%p A141114 filter:= proc(n) uses numtheory;
%p A141114   igcd(tau(tau(n)), n) = 1
%p A141114 end proc:
%p A141114 select(filter, [$1..200]); # _Robert Israel_, Dec 16 2019
%t A141114 Select[Range[200], GCD[DivisorSigma[0, DivisorSigma[0, # ]], # ] == 1 &] (* _Stefan Steinerberger_, Jun 05 2008 *)
%o A141114 (Magma) [k:k in [1..130]|Gcd(k,#Divisors(#Divisors(k))) eq 1]; // _Marius A. Burtea_, Dec 16 2019
%o A141114 (PARI) is(n) = gcd(numdiv(numdiv(n)), n)==1 \\ _Felix Fröhlich_, Dec 16 2019
%Y A141114 Cf. A010553, A141113, A141115.
%K A141114 nonn
%O A141114 1,2
%A A141114 _Leroy Quet_, Jun 04 2008
%E A141114 More terms from _Stefan Steinerberger_, Jun 05 2008