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A059886 a(n) = |{m : multiplicative order of 4 mod m=n}|. 8
2, 2, 4, 4, 6, 16, 6, 8, 26, 38, 14, 68, 6, 54, 84, 16, 6, 462, 6, 140, 132, 110, 14, 664, 120, 118, 128, 188, 62, 4456, 6, 96, 364, 118, 498, 7608, 30, 118, 180, 568, 30, 9000, 30, 892, 3974, 494, 62, 5360, 24, 8024, 1524, 892, 62, 9600, 3050, 1784, 372, 446 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The multiplicative order of a mod m, GCD(a,m)=1, is the smallest natural number d for which a^d = 1 (mod m).

a(n) is the number of orders of degree-n monic irreducible polynomials over GF(4).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..160

FORMULA

a(n) = Sum_{ d divides n } mu(n/d)*tau(4^d-1), (mu(n) = Moebius function A008683, tau(n) = number of divisors of n A000005).

EXAMPLE

a(1) = |{1,3}| = 2, a(2) = |{5,15}| =2, a(3) = |{7,9,21,63}| =4, a(4) = |{17,51,85,255}| = 4.

MAPLE

with(numtheory):

a:= n-> add(mobius(n/d)*tau(4^d-1), d=divisors(n)):

seq(a(n), n=1..60);  # Alois P. Heinz, Oct 12 2012

MATHEMATICA

a[n_] := DivisorSum[n, MoebiusMu[n/#]*DivisorSigma[0, 4^# - 1]&]; Array[a, 100] (* Jean-François Alcover, Nov 11 2015 *)

CROSSREFS

Cf. A000005, A008683, A027377, A053447, A058948, A059499, A059885, A059887-A059892.

Column k=4 of A212957. - Alois P. Heinz, Oct 12 2012

Sequence in context: A066813 A033732 A033752 * A272339 A267261 A219027

Adjacent sequences:  A059883 A059884 A059885 * A059887 A059888 A059889

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 06 2001

STATUS

approved

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Last modified February 19 05:12 EST 2018. Contains 299330 sequences. (Running on oeis4.)