%I #9 Feb 23 2013 13:33:49

%S 1,1,1,1,1,1,2,2,2,2,4,2,2,2,2,4,4,2,6,4,2,4,10,4,4,4,6,4,6,4,8,8,4,8,

%T 4,4,6,6,4,8,8,4,12,8,4,10,22,8,12,8,8,8,12,6,8,8,6,12,28,8,8,8,6,16,

%U 8,8,20,16,10,8,24,8,12,12,8,12,8,8,24,16,18,16,40,8,16,12

%N phi(delta(n)), n >= 1, with phi = A000010 (Euler's totient) and delta = A055034 (degree of minimal polynomials with coefficients given in A187360).

%C If n belongs to A206551 (cyclic multiplicative group Modd n) then there exist precisely a(n) primitive roots Modd n. For these n values the number of entries in row n of the table A216319 with value delta(n) (the row length) is a(n). Note that a(n) is also defined for the complementary n values from A206552 (non-cyclic multiplicative group Modd n) for which no primitive root Modd n exists.

%C See also A216322 for the number of primitive roots Modd n.

%F a(n) = phi(delta(n)), n >= 1, with phi = A000010 (Euler's totient) and delta = A055034 with delta(1) = 1 and delta(n) = phi(2*n)/2 if n >= 2.

%e a(8) = 2 because delta(8) = 4 and phi(4) = 2. There are 2 primitive roots Modd 8, namely 3 and 5 (see the two 4s in row n=8 of A216320). 8 = A206551(8).

%e a(12) = 2 because delta(12) = 4 and phi(4) = 2. But there is no primitive root Modd 12, because 4 does not show up in row n=12 of A216320. 12 = A206552(1).

%o (PARI) a(n)=eulerphi(ceil(eulerphi(2*n)/2)) \\ _Charles R Greathouse IV_, Feb 21 2013

%Y Cf. A000010, A055034, A216319, A216320, A216322, A010554 (analog in modulo n case).

%K nonn

%O 1,7

%A _Wolfdieter Lang_, Sep 21 2012