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A059885 a(n) = |{m : multiplicative order of 3 mod m = n}|. 16
2, 2, 2, 6, 4, 10, 2, 14, 4, 16, 6, 58, 2, 10, 16, 88, 6, 108, 6, 150, 10, 54, 6, 290, 18, 10, 56, 138, 14, 716, 14, 144, 22, 118, 40, 1088, 6, 54, 90, 670, 14, 730, 6, 570, 356, 22, 30, 13864, 124, 342, 54, 138, 14, 3912, 116, 1362, 118, 238, 6, 22058, 6, 110 (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) = number of orders of degree-n monic irreducible polynomials over GF(3).

LINKS

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

FORMULA

a(n) = Sum_{ d divides n } mu(n/d)*tau(3^d-1), (mu(n) = Moebius function A008683, tau(n) = number of divisors of n A000005).

EXAMPLE

a(2) = |{4,8}| = 2, a(4) = |{5,10,16,20,40,80}| = 6, a(6) = |{7,14,28,52,56,91,104,182,364,728}| = 10.

MAPLE

with(numtheory); A059885 := proc(n) local d, s; s := 0; for d in divisors(n) do s := s+mobius(n/d)*tau(3^d-1); od; RETURN(s); end;

MATHEMATICA

a[n_] := Sum[ MoebiusMu[n/d] * DivisorSigma[0, 3^d - 1], {d, Divisors[n]}]; Table[a[n], {n, 1, 62} ] (* Jean-François Alcover, Dec 12 2012 *)

CROSSREFS

Cf. A000005, A008683, A027376, A058944, A059499, A059886-A059892, A212906.

Column k=3 of A212957. - Alois P. Heinz, Oct 12 2012

Sequence in context: A278264 A232114 A038074 * A259689 A246707 A211391

Adjacent sequences:  A059882 A059883 A059884 * A059886 A059887 A059888

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 06 2001

STATUS

approved

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Last modified February 25 11:08 EST 2018. Contains 299653 sequences. (Running on oeis4.)