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A062373 Ratio of totient to Carmichael's lambda function is 2. 15
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A033949 A175594 A272592 * A180690 A194592 A175132
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jun 17 2001
EXTENSIONS
More terms from Reiner Martin, Dec 22 2001
STATUS
approved

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Last modified March 19 02:51 EDT 2024. Contains 370952 sequences. (Running on oeis4.)