OFFSET
1,1
COMMENTS
In Schick's book these are the B values, the number of periodic sequences, for the odd numbers N with B values >= 2. These numbers N are given in A333855.
In the complete coach system Sigma(b) of Hilton and Pedersen, these are the number of coaches for the odd numbers b from A333855 with more than one coach.
These are also the number of periodic modified doubling sequences for the odd numbers b from A333855 given in comments and examples by Gary W. Adamson, see his Aug 25 2019 comment in A065941, where this is named "r-t table" (for roots trajectory).
REFERENCES
Peter Hilton and Jean Pedersen, A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics, Cambridge University Press, 2010, pp. 261-264.
Carl Schick, Trigonometrie und unterhaltsame Zahlentheorie, Bokos Druck, Zürich, 2003 (ISBN 3-9522917-0-6). Tables 3.1 to 3.10, for odd p = 3..113 (with gaps), pp. 158-166.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Wolfdieter Lang, On the Equivalence of Three Complete Cyclic Systems of Integers, arXiv:2008.04300 [math.NT], 2020.
EXAMPLE
MATHEMATICA
Map[EulerPhi[#2]/(2 If[#2 > 1 && GCD[#1, #2] == 1, Min[MultiplicativeOrder[#1, #2, {-1, 1}]], 0]) & @@ {2, #} &, 1 + 2 Select[Range[2, 15000], 2 <= EulerPhi[#2]/(2 If[#2 > 1 && GCD[#1, #2] == 1, Min[MultiplicativeOrder[#1, #2, {-1, 1}]], 0]) & @@ {2, 2 # + 1} &]] (* Michael De Vlieger, Oct 15 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Jun 29 2020
STATUS
approved