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A282623 Number of independent cycles of the multiplicative group of integers modulo A033949(n). 2
3, 3, 4, 4, 4, 3, 7, 3, 4, 5, 3, 4, 3, 4, 10, 3, 3, 4, 10, 6, 4, 4, 7, 3, 10, 12, 6, 6, 3, 6, 3, 4, 7, 4, 3, 3, 4, 16, 7, 10, 4, 7, 4, 16, 3, 3, 4, 13, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A cycle starting with number a of the restricted residue system modulo m (namely the one with the smallest positive numbers RRS(m)) is independent of a cycle starting with number b != a if the set of numbers of the a-cycle is not a (not necessarily proper) subset of the numbers of the b-cycle.

See Table 7, column 4 of the W. Lang link for these numbers.

See also the Table in the W. Lang link given in A282624 for these independent cycles.

LINKS

Table of n, a(n) for n=1..50.

Wolfdieter Lang, The field Q(2cos(pi/n)), its Galois group and length ratios in the regular n-gon, arXiv:1210.1018 [math.GR], 2012.

EXAMPLE

a(1) = 3 because A033949(1) = 8 with RRS(8) = {1, 3, 5, 7} and the three 2-cycles [3,1],[5,1] and [7,1], which are independent.

a(4) = 4 because A033949(4) = 16 with RRS(16) = {1, 3, 5, 7, 9, 11, 13, 15} and only, e.g., the cycles from 3, 5, 7 and 15 are independent. The cycles [1], [9, 1], [11, 9, 3, 1] and [13, 9, 5, 1] are not independent. One could replace 5 with 13 but we always take the smallest numbers.

CROSSREFS

Cf. A033949, A282624.

Sequence in context: A057690 A318706 A298199 * A090589 A163400 A090972

Adjacent sequences:  A282620 A282621 A282622 * A282624 A282625 A282626

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Mar 03 2017

STATUS

approved

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)