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A206552 Moduli n for which the multiplicative group Modd n is non-cyclic (acyclic). 5
12, 20, 24, 28, 30, 36, 40, 42, 44, 48, 52, 56, 60, 63, 65, 66, 68, 70, 72, 76, 78, 80, 84, 85, 88, 90, 91, 92, 96, 100, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 124, 126, 130, 132, 133, 136, 138, 140, 144, 145, 148, 150, 152, 154, 156, 160, 164, 165 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For Modd n (not to be confused with mod n) see a comment on A203571.

Precisely these numbers n (only the ones <=165 are shown above) have no primitive root Modd n. See the zero entries of A206550, except A206550(1) = 0 which stands for a primitive root 0.

The multiplicative Modd n group is the Galois group Gal(Q(rho(n))/Q), with the algebraic number rho(n) := 2*cos(Pi/n) with minimal polynomial C(n,x), whose coefficients are given in A187360.

LINKS

Table of n, a(n) for n=1..58.

FORMULA

A206550(a(n)) = 0, n>=1.

EXAMPLE

a(1) = 12 because A206550(12) = 0 for the first time, not counting A206550(1) = 0. The cycle structure of the multiplicative Modd 12 group is [[5,1],[7,1],[11,1]]. This is the (abelian, non-cyclic) group Z_2 x Z_2 (isomorphic to the Klein group V_4 or Dih_2).

a(2) = 20 because A206550(20) = 0 for the second time, not counting A206550(1) = 0. The cycle structure of the multiplicative Modd 20 group is [[3,9,13,1],[7,9,17,1],[11,1],[19,1]]. This is the (abelian, non-cyclic) group Z_4 x Z_2.

CROSSREFS

Cf. A206550, A206551, A033949 (mod n case).

Sequence in context: A075078 A050421 A307517 * A332832 A065201 A136724

Adjacent sequences:  A206549 A206550 A206551 * A206553 A206554 A206555

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Mar 27 2012

STATUS

approved

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Last modified September 28 11:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)