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 A059885 a(n) = |{m : multiplicative order of 3 mod m = n}|. 16

%I

%S 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,

%T 56,138,14,716,14,144,22,118,40,1088,6,54,90,670,14,730,6,570,356,22,

%U 30,13864,124,342,54,138,14,3912,116,1362,118,238,6,22058,6,110

%N a(n) = |{m : multiplicative order of 3 mod m = n}|.

%C 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).

%H Alois P. Heinz, <a href="/A059885/b059885.txt">Table of n, a(n) for n = 1..100</a>

%F 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).

%e 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.

%p 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;

%t 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 *)

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

%Y Column k=3 of A212957. - _Alois P. Heinz_, Oct 12 2012

%K easy,nonn

%O 1,1

%A _Vladeta Jovovic_, Feb 06 2001

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Last modified November 17 00:14 EST 2018. Contains 317275 sequences. (Running on oeis4.)