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A219029 n - 1 - phi(phi(n)). 3

%I

%S -1,0,1,2,2,4,4,5,6,7,6,9,8,11,10,11,8,15,12,15,16,17,12,19,16,21,20,

%T 23,16,25,22,23,24,25,26,31,24,31,30,31,24,37,30,35,36,35,24,39,36,41,

%U 34,43,28,47,38,47,44,45,30,51,44,53,50,47,48,57,46,51,48

%N n - 1 - phi(phi(n)).

%C There are exactly n - 1 - phi(phi(n)) non-primitive roots for n, less than n, if n is prime.

%C a(n) will be the same as A219027(n) except when n is a member of A033949 or n = 1, i.e. n is not 2, 4, prime, power of a prime, twice a prime, or twice a prime power.

%H Vincenzo Librandi, <a href="/A219029/b219029.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n - 1 - A010554(n). - _V. Raman_, Nov 22 2012

%t Table[n - (EulerPhi[EulerPhi[n]] + 1), {n, 75}] (* _Alonso del Arte_, Nov 17 2012 *)

%o (PARI) for(n=1,100,print1(n-1-eulerphi(eulerphi(n))","))

%o (MAGMA) [(n - 1 - EulerPhi(EulerPhi(n))): n in [1..70] ]; // _Vincenzo Librandi_, Jan 26 2013

%Y Cf. A008330 (number of primitive roots for the n-th prime).

%Y Cf. A046144 (number of primitive roots for n).

%Y Cf. A010554 (value of phi(phi(n))).

%Y Cf. A219027, A219428.

%K sign

%O 1,4

%A _V. Raman_, Nov 10 2012

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Last modified September 30 12:21 EDT 2020. Contains 337439 sequences. (Running on oeis4.)