A216321 phi(delta(n)), n >= 1, with phi = A000010 (Euler's totient) and delta = A055034 (degree of minimal polynomials with coefficients given in A187360).

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

Offset

1,7

Comments

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.

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

Links

Table of n, a(n) for n=1..86.

Formula

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.

Example

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).
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).

Prog

(PARI) a(n)=eulerphi(ceil(eulerphi(2*n)/2)) \\ Charles R Greathouse IV, Feb 21 2013

Crossrefs

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

Sequence in context: A122066 A053238 A227783 * A058263 A232398 A048669

Adjacent sequences: A216318 A216319 A216320 * A216322 A216323 A216324

Keyword

nonn

Author

Wolfdieter Lang, Sep 21 2012

Status

approved