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).
Also, number of primitive factors of 3^n - 1 (cf. A218356). - Max Alekseyev, May 03 2022
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..690 (first 100 terms from Alois P. Heinz)
FORMULA
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
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 06 2001
STATUS
approved