A059889 - OEIS

%I #19 Sep 11 2022 12:45:18

%S 4,6,8,26,4,42,12,48,52,66,12,778,4,138,80,300,12,528,12,1430,72,138,

%T 28,15216,24,66,1216,966,28,3630,28,1344,360,58,108,16988,28,138,176,

%U 12752,28,7398,12,4422,1900,122,12,131028,240,536,744,1046,28,23744,44

%N a(n) = |{m : multiplicative order of 7 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).

%C a(n) = number of orders of degree n monic irreducible polynomials over GF(7).

%C Also, number of primitive factors of 7^n - 1 (cf. A218358). - _Max Alekseyev_, May 03 2022

%H Max Alekseyev, <a href="/A059889/b059889.txt">Table of n, a(n) for n = 1..388</a>

%F a(n) = Sum_{d|n} mu(n/d)*tau(7^d-1), (mu(n) = Moebius function A008683, tau(n) = number of divisors of n A000005).

%p with(numtheory):

%p a:= n-> add(mobius(n/d)*tau(7^d-1), d=divisors(n)):

%p seq(a(n), n=1..40);  # _Alois P. Heinz_, Oct 12 2012

%Y Number of primitive factors of b^n - 1: A059499 (b=2), A059885(b=3), A059886 (b=4), A059887 (b=5), A059888 (b=6), this sequence (b=7), A059890 (b=8), A059891 (b=9), A059892 (b=10).

%Y Cf. A000005, A008683, A058946, A053450, A057954, A058946, A074249, A212486, A218358

%Y Column k=7 of A212957.

%K nonn

%O 1,1

%A _Vladeta Jovovic_, Feb 06 2001