A317013 For successive terms of A002202, totient values t, lcm({x: phi(x)=t})/gcd({x: phi(x)=t}).

2, 12, 120, 126, 240, 2, 3276, 8160, 1026, 3300, 2, 32760, 2, 2, 16320, 531468, 270600, 4214, 12, 2, 65520, 2, 2, 12, 2, 5241852, 32640, 2, 2, 5043631320, 2, 541200, 2, 25284, 245640, 12, 216084960, 25250, 2, 12, 2, 4697028, 2, 393240, 12, 3407203800, 2, 65280, 2, 388332

Offset: 1

Author

Michel Marcus, Jul 19 2018

Keywords

• nonn

Comments

From Torlach Rush, Jul 03 2018: (Start)

Consider the quotients q(t) = lcm({x: phi(x)=t})/gcd({x: phi(x)=t}).

When the number of solutions is 2, q(t) must be 2. For example invphi(10) = [11, 22], and q(10)=2.

When the number of solutions is 3, the solutions are x1 < x2 < (2 * x1) and the only observed value of q(t) is 12. For example, invphi(44) = [69, 92, 138], and q(44)=12.

When the number of solutions is greater than 3, multiple values of q(t) are observed. (End)

Examples

			invphi(1) = [1, 2] and lcm(1, 2) / gcd(1, 2) is 2.
		

Links

• Max Alekseyev, PARI scripts for various problems

Crossrefs

Cf. A000010, A002202, A032447.

Programs

Mathematica

Map[LCM[##]/GCD[##] & @@ # &, Take[Values@ KeySort@ PositionIndex@ Array[EulerPhi, 10^6], 50]] (* Michael De Vlieger, Jul 20 2018 *)

PARI

lista(nn) = {for (n=1, nn, my(v = invphi(n)); if (#v, print1(lcm(v)/gcd(v), ", ")););}