A356497 a(n) = maximal 2^k such that there exists a (2^k)-th root of unity modulo n.

1, 1, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 4, 2, 4, 4, 16, 2, 2, 4, 2, 2, 2, 2, 4, 4, 2, 2, 4, 4, 2, 8, 2, 16, 4, 2, 4, 2, 4, 4, 8, 2, 2, 2, 4, 2, 2, 4, 2, 4, 16, 4, 4, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 16, 4, 2, 2, 16, 2, 4, 2, 2, 8, 4, 4, 2, 2, 4, 2, 4, 2, 8, 2, 2, 16, 2, 4, 2, 8, 4, 4, 2, 2, 2, 4, 8, 32, 2, 2, 4

Offset

1,3

Links

Table of n, a(n) for n=1..100.

Mathematica

MaxOrdPowTwo[n_] := MaximalBy[Select[Table[{k, MultiplicativeOrder[k, n]}, {k, n}], IntegerQ@Log2@#[[2]] &], Last][[1, 2]];
MaxOrdPowTwoConjectured[n_] := 2^IntegerExponent[CarmichaelLambda[n], 2]; (* conjectured *)

Crossrefs

Sequence in context: A289827 A092188 A340675 * A097884 A094818 A114233

Adjacent sequences: A356494 A356495 A356496 * A356498 A356499 A356500

Keyword

nonn

Author

Dmitry Grekov, Aug 09 2022

Status

approved