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A062373 Ratio of totient to Carmichael's lambda function is 2. 15

%I #28 Oct 30 2022 18:19:59

%S 8,12,15,16,20,21,28,30,32,33,35,36,39,42,44,45,51,52,55,57,64,66,68,

%T 69,70,75,76,77,78,87,90,92,93,95,99,100,102,108,110,111,114,115,116,

%U 119,123,124,128,129,135,138,141,143,147,148,150,153,154,155,159,161

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

%C 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

%C 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

%H R. J. Mathar, <a href="/A062373/b062373.txt">Table of n, a(n) for n = 1..20000</a>

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

%e From _Jianing Song_, Jul 28 2018: (Start)

%e (Z/8Z)* = C_2 X C_2, so 8 is a term.

%e (Z/21Z)* = C_2 X C_6, so 21 is a term.

%e (Z/35Z)* = C_2 X C_12, so 35 is a term. (End)

%t Reap[ For[ n = 1, n <= 161, n++, If[ EulerPhi[n] / CarmichaelLambda[n] == 2, Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Mar 26 2013 *)

%t Select[Range[200],EulerPhi[#]/CarmichaelLambda[#]==2&] (* _Harvey P. Dale_, Jun 27 2018 *)

%o (Haskell)

%o a062373 n = a062373_list !! (n-1)

%o a062373_list = filter ((== 2) . a034380) [1..]

%o -- _Reinhard Zumkeller_, Sep 02 2014

%o (PARI) isok(n) = eulerphi(n)/lcm(znstar(n)[2]) == 2; \\ _Michel Marcus_, Jul 28 2018

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

%K easy,nonn

%O 1,1

%A _Vladeta Jovovic_, Jun 17 2001

%E More terms from _Reiner Martin_, Dec 22 2001

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)