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

6, 12, 15, 18, 21, 24, 30, 33, 36, 39, 45, 48, 51, 54, 55, 57, 60, 63, 66, 69, 72, 75, 87, 90, 91, 93, 95, 96, 99, 102, 108, 110, 111, 117, 120, 123, 129, 132, 135, 138, 141, 144, 145, 147, 150, 153, 155, 159, 162, 165, 171, 174, 177, 180, 182, 183, 189, 190, 192, 198, 201

Offset: 1

Author

Torlach Rush, Mar 05 2019

Keywords

• nonn

Comments

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

Examples

			6 is a term because gcd(6,2) <> gcd(6,12).
12 is a term because gcd(12,4) <> gcd(12, 24).
13 is not a term because gcd(13,12) = gcd(13, 14).
14 is not a term because gcd(14,6) = gcd(14, 24).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Complement of A306528.

Cf. A306695.

Programs

Maple

psi:= k -> mul((t+1)/t, t=numtheory:-factorset(k))*k:
select(t -> igcd(t, psi(t)) <> igcd(t, numtheory:-phi(t)), [$1..1000]); # Robert Israel, Apr 28 2019

PARI

dpsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
isok(k) = gcd(k, eulerphi(k)) != gcd(k, dpsi(k)); \\ Michel Marcus, Mar 21 2019