

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
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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 acycle is not a (not necessarily proper) subset of the numbers of the bcycle.
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 ngon, arXiv:1210.1018 [math.GR], 2012.


EXAMPLE

a(1) = 3 because A033949(1) = 8 with RRS(8) = {1, 3, 5, 7} and the three 2cycles [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



