A059888 - OEIS

%I #13 May 03 2022 11:28:22

%S 2,2,2,4,4,10,2,8,12,40,6,108,6,42,40,48,30,100,6,332,10,22,30,376,26,

%T 118,48,332,2,1436,6,448,54,222,88,7952,62,54,54,2680,6,698,30,476,

%U 1476,222,14,7632,28,438,478,1916,14,1872,84,11896,118,58,14,784452

%N a(n) = |{m : multiplicative order of 6 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 Also, number of primitive factors of 6^n - 1. - _Max Alekseyev_, May 03 2022

%H Max Alekseyev, <a href="/A059888/b059888.txt">Table of n, a(n) for n = 1..420</a>

%F a(n) = Sum_{ d divides n } mu(n/d)*tau(6^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(6^d-1), d=divisors(n)):

%p seq(a(n), n=1..50);  # _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), this sequence (b=6), A059889 (b=7), A059890 (b=8), A059891 (b=9), A059892 (b=10).

%Y Column k=6 of A212957.

%Y Cf. A000005, A008683, A053449, A057955, A274907.

%K nonn

%O 1,1

%A _Vladeta Jovovic_, Feb 06 2001