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Numbers k such that gcd(k, phi(k)) = tau(k).
1

%I #21 Sep 08 2022 08:45:05

%S 1,8,9,18,24,40,56,84,88,104,136,152,156,184,228,232,248,296,328,344,

%T 360,372,376,424,444,472,488,516,536,568,584,632,664,712,732,776,792,

%U 804,808,824,856,872,876,904,948,1016,1048,1096,1112,1164,1192,1208

%N Numbers k such that gcd(k, phi(k)) = tau(k).

%H Georg Fischer, <a href="/A069809/b069809.txt">Table of n, a(n) for n = 1..2000</a> (first 1835 terms by Marius A. Burtea)

%t Select[Range[1300], GCD[#, EulerPhi[#]] == DivisorSigma[0, #] &] (* _Jayanta Basu_, Mar 21 2013 *)

%o (PARI) for(n=1,1592,if(gcd(n,eulerphi(n))==numdiv(n),print1(n,",")))

%o (Magma) [n: n in [1..2000] | GCD(n,EulerPhi(n)) eq NumberOfDivisors(n) ];// _Marius A. Burtea_, Dec 28 2018

%Y Cf. A000005, A000010, A009195.

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Apr 30 2002