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Integers m such that both phi(m) and sigma(m) are coprime to tau(m).
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%I #13 Aug 08 2020 11:30:11

%S 1,2,4,16,25,64,81,100,121,256,289,484,529,729,841,1024,1156,1296,

%T 1600,1681,2116,2209,2401,2809,3025,3364,3481,4096,4624,5041,5184,

%U 6400,6724,6889,7225,7921,8464,8836,10201,11236,11449,11664,12100,12769,13225,13456,13924

%N Integers m such that both phi(m) and sigma(m) are coprime to tau(m).

%H Amiram Eldar, <a href="/A298080/b298080.txt">Table of n, a(n) for n = 1..10000</a>

%H Jean-Marie De Koninck and Imre Kátai, <a href="https://www.emis.de/journals/PIMB/101/9.html">On the coprimality of some arithmetic functions</a>, Publications de l'Institut Mathématique, 2010 87(101):121-128.

%t Select[Range[14000], CoprimeQ[EulerPhi[#], (d = DivisorSigma[0, #])] && CoprimeQ[DivisorSigma[1, #], d] &] (* _Amiram Eldar_, Aug 08 2020 *)

%o (PARI) isok(n) = (gcd(eulerphi(n), numdiv(n))==1) && (gcd(sigma(n), numdiv(n)) == 1);

%Y Intersection of A046678 and A225983.

%K nonn

%O 1,2

%A _Michel Marcus_, Jan 12 2018