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

1,1

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

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).

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A032043 A200561 A241380 * A179478 A051548 A110660

Adjacent sequences: A028473 A028474 A028475 * A028477 A028478 A028479

Keyword

nonn,changed

Author

Vladeta Jovovic, Jan 12 2002

Status

approved