A028476 Greatest k such that phi(k) = phi(n), where phi is Euler's totient function.

2, 2, 6, 6, 12, 6, 18, 12, 18, 12, 22, 12, 42, 18, 30, 30, 60, 18, 54, 30, 42, 22, 46, 30, 66, 42, 54, 42, 58, 30, 62, 60, 66, 60, 90, 42, 126, 54, 90, 60, 150, 42, 98, 66, 90, 46, 94, 60, 98, 66, 120, 90, 106, 54, 150, 90, 126, 58, 118, 60, 198, 62, 126, 120, 210, 66, 134

Offset: 1

Author

Vladeta Jovovic, Jan 12 2002

Keywords

• nonn

Comments

Every number in this sequence occurs at least twice. For all n > 6, a(n) > phi(n)^2 is impossible. - Alonso del Arte, Dec 31 2016

Examples

			phi(1) = 1 and phi(2) = 1 also. There is no greater k such that phi(k) = 1, so therefore a(1) = a(2) = 2.
phi(3) = phi(4) = phi(6) = 2, and there is no greater k such that phi(k) = 6, hence a(3) = a(4) = a(6) = 6.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (computed from the b-file of A057826 provided by T. D. Noe)
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000010, A015126, A057826, A066412, A066659, A071181.

Programs

Mathematica

Table[Module[{k = (2 Boole[n <= 6]) + #^2}, While[EulerPhi@ k != #, k--]; k] &@ EulerPhi@ n, {n, 120}] (* Michael De Vlieger, Dec 31 2016 *)

PARI

a(n) = invphiMax(eulerphi(n)); \\ Amiram Eldar, Nov 14 2024, using Max Alekseyev's invphi.gp

Formula

a(1) = a(2) = 2, for n > 2, a(n) = A057826(A000010(n)/2). - Antti Karttunen, Aug 07 2017