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A216321 phi(delta(n)), n >= 1, with phi = A000010 (Euler's totient) and delta = A055034 (degree of minimal polynomials with coefficients given in A187360). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 15 12:59 EDT 2020. Contains 336502 sequences. (Running on oeis4.)