%I #27 Apr 28 2019 20:08:57

%S 6,12,15,18,21,24,30,33,36,39,45,48,51,54,55,57,60,63,66,69,72,75,87,

%T 90,91,93,95,96,99,102,108,110,111,117,120,123,129,132,135,138,141,

%U 144,145,147,150,153,155,159,162,165,171,174,177,180,182,183,189,190,192,198,201

%N Numbers k such that gcd(k, phi(k)) <> gcd(k, psi(k)).

%C Numbers m such that A306695(m) = m are terms.

%H Robert Israel, <a href="/A306711/b306711.txt">Table of n, a(n) for n = 1..10000</a>

%e 6 is a term because gcd(6,2) <> gcd(6,12).

%e 12 is a term because gcd(12,4) <> gcd(12, 24).

%e 13 is not a term because gcd(13,12) = gcd(13, 14).

%e 14 is not a term because gcd(14,6) = gcd(14, 24).

%p psi:= k -> mul((t+1)/t, t=numtheory:-factorset(k))*k:

%p select(t -> igcd(t, psi(t)) <> igcd(t, numtheory:-phi(t)), [$1..1000]); # _Robert Israel_, Apr 28 2019

%o (PARI) dpsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615

%o isok(k) = gcd(k, eulerphi(k)) != gcd(k, dpsi(k)); \\ _Michel Marcus_, Mar 21 2019

%Y Cf. A000010 (Euler totient function), A001615 (Dedekind psi function).

%Y Complement of A306528.

%Y Cf. A306695.

%K nonn

%O 1,1

%A _Torlach Rush_, Mar 05 2019