A062373 Ratio of totient to Carmichael's lambda function is 2.

8, 12, 15, 16, 20, 21, 28, 30, 32, 33, 35, 36, 39, 42, 44, 45, 51, 52, 55, 57, 64, 66, 68, 69, 70, 75, 76, 77, 78, 87, 90, 92, 93, 95, 99, 100, 102, 108, 110, 111, 114, 115, 116, 119, 123, 124, 128, 129, 135, 138, 141, 143, 147, 148, 150, 153, 154, 155, 159, 161

Offset: 1

Author

Vladeta Jovovic, Jun 17 2001

Keywords

• easy
• nonn

Comments

Numbers k such that the highest order of elements in (Z/kZ)* is phi(n)/2, (Z/kZ)* = the multiplicative group of integers modulo k. Also numbers k such that (Z/kZ)* = C_2 X C_(2r). - Jianing Song, Jul 28 2018

Contains the powers of 2 greater than 4, 4 times primes, and semiprimes pq where (p-1)/2 and (q-1)/2 are coprime. If n is odd and in this sequence then so is 2n. - Charlie Neder, May 27 2019

Examples

			From _Jianing Song_, Jul 28 2018: (Start)
(Z/8Z)* = C_2 X C_2, so 8 is a term.
(Z/21Z)* = C_2 X C_6, so 21 is a term.
(Z/35Z)* = C_2 X C_12, so 35 is a term. (End)
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000010, A002322, A034380, A033948, A062374, A062375, A062376, A062377.

Programs

Haskell

a062373 n = a062373_list !! (n-1)
a062373_list = filter ((== 2) . a034380) [1..]
-- Reinhard Zumkeller, Sep 02 2014

Mathematica

Reap[ For[ n = 1, n <= 161, n++, If[ EulerPhi[n] / CarmichaelLambda[n] == 2, Sow[n]]]][[2, 1]] (* Jean-François Alcover, Mar 26 2013 *)
Select[Range[200],EulerPhi[#]/CarmichaelLambda[#]==2&] (* Harvey P. Dale, Jun 27 2018 *)

PARI

isok(n) = eulerphi(n)/lcm(znstar(n)[2]) == 2; \\ Michel Marcus, Jul 28 2018

Formula

Solutions to phi(k)/lambda(k) = 2.

Extensions

More terms from Reiner Martin, Dec 22 2001