|
Search: id:A046790
|
|
|
| A046790 |
|
Arithmetic and geometric means of A046791(n) and a(n) both integers. |
|
+0
5
|
|
| 8, 9, 16, 18, 24, 25, 27, 32, 36, 40, 45, 48, 49, 50, 54, 56, 63, 64, 72, 75, 80, 81, 88, 90, 96, 98, 99, 100, 104, 108, 112, 117, 120, 121, 125, 126, 128, 135, 136, 144, 147, 150, 152, 153, 160, 162, 168, 169, 171, 175, 176, 180, 184, 189, 192, 196, 198, 200, 207, 208
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
n such that A008475(n) is different from A001414(n). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 11 2003
This sequence appears to coincide with the sequence of moduli n for which there exist affine maps f:x->a x + b modulo n, with a>1, such that f has order n in the affine group. - Emmanuel Amiot (manu.amiot(AT)free.fr), Jul 28 2007
|
|
REFERENCES
|
Amiot, E., AutoSimilar Melodies, Journal of Mathematics and Music, Taylor & Francis, to appear.
|
|
EXAMPLE
|
8 is in the list because f:x->5x+1 mod 8 is a map with order 8 in the group of affine maps mod 8: the smallest power of f equal to identity is f^8. Obviously the maps x->x+1 always have this property, so are excluded from consideration.
|
|
MATHEMATICA
|
ordreMax[a_, n_]:= Module[{mo, r, s, s0, gcd}, mo=MultiplicativeOrder[a, n]; s= s0=Mod[Sum[a^k, {k, 0, mo-1}], n]; Max[Table[gcd=GCD[a-1, b]; r=1; While[Mod[s *gcd, n]!=0, s=Mod[s0+a^mos, n]; r++ ]; r*mo, {b, 0, n-1} ]] ] ordreMax[n_] := Module[{candidats, m, t}, candidats = Select[Range[2, n-1], (GCD[n, # ]==1 && GCD[n, #-1]>1)&]; m=Max[t=Table[ordreMax[a, n], {a, candidats}] ]; {m, Part[candidats, Flatten@Position[t, m] ]}] Module[{resu}, Do[resu=ordreMax[n]; If[First[resu] >=n, Print[n ]], {n, 4, 200}]] - Emmanuel Amiot (manu.amiot(AT)free.fr), Jul 28 2007
|
|
CROSSREFS
|
Adjacent sequences: A046787 A046788 A046789 this_sequence A046791 A046792 A046793
Sequence in context: A079669 A047393 A037371 this_sequence A057111 A022098 A129659
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
David W. Wilson (davidwwilson(AT)comcast.net)
|
|
|
Search completed in 0.002 seconds
|
