A282623 Number of independent cycles of the multiplicative group of integers modulo A033949(n).

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

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], 2012-2017.

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,more

Author

Wolfdieter Lang, Mar 03 2017

Status

approved