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

1,1

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

Links

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

Formula

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

Example

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)

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 *)

Prog

(Haskell)
a062373 n = a062373_list !! (n-1)
a062373_list = filter ((== 2) . a034380) [1..]
-- Reinhard Zumkeller, Sep 02 2014
(PARI) isok(n) = eulerphi(n)/lcm(znstar(n)[2]) == 2; \\ Michel Marcus, Jul 28 2018

Crossrefs

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

Sequence in context: A033949 A175594 A272592 * A180690 A194592 A175132

Adjacent sequences: A062370 A062371 A062372 * A062374 A062375 A062376

Keyword

easy,nonn

Author

Vladeta Jovovic, Jun 17 2001

Extensions

More terms from Reiner Martin, Dec 22 2001

Status

approved