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A046790
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Arithmetic and geometric means of A046791(n) and a(n) both integers.
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5
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
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REFERENCES
| Amiot, E., AutoSimilar Melodies, Journal of Mathematics and Music, Taylor & Francis, to appear.
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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.
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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
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CROSSREFS
| Sequence in context: A079669 A047393 A037371 * A057111 A171425 A143720
Adjacent sequences: A046787 A046788 A046789 * A046791 A046792 A046793
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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