cp's OEIS Frontend

A306711 Numbers k such that gcd(k, phi(k)) <> gcd(k, psi(k)).

%I A306711 #27 Apr 28 2019 20:08:57
%S A306711 6,12,15,18,21,24,30,33,36,39,45,48,51,54,55,57,60,63,66,69,72,75,87,
%T A306711 90,91,93,95,96,99,102,108,110,111,117,120,123,129,132,135,138,141,
%U A306711 144,145,147,150,153,155,159,162,165,171,174,177,180,182,183,189,190,192,198,201
%N A306711 Numbers k such that gcd(k, phi(k)) <> gcd(k, psi(k)).
%C A306711 Numbers m such that A306695(m) = m are terms.
%H A306711 Robert Israel, <a href="/A306711/b306711.txt">Table of n, a(n) for n = 1..10000</a>
%e A306711 6 is a term because gcd(6,2) <> gcd(6,12).
%e A306711 12 is a term because gcd(12,4) <> gcd(12, 24).
%e A306711 13 is not a term because gcd(13,12) = gcd(13, 14).
%e A306711 14 is not a term because gcd(14,6) = gcd(14, 24).
%p A306711 psi:= k -> mul((t+1)/t, t=numtheory:-factorset(k))*k:
%p A306711 select(t -> igcd(t, psi(t)) <> igcd(t, numtheory:-phi(t)), [$1..1000]); # _Robert Israel_, Apr 28 2019
%o A306711 (PARI) dpsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
%o A306711 isok(k) = gcd(k, eulerphi(k)) != gcd(k, dpsi(k)); \\ _Michel Marcus_, Mar 21 2019
%Y A306711 Cf. A000010 (Euler totient function), A001615 (Dedekind psi function).
%Y A306711 Complement of A306528.
%Y A306711 Cf. A306695.
%K A306711 nonn
%O A306711 1,1
%A A306711 _Torlach Rush_, Mar 05 2019