This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A059888 #21 Apr 15 2025 22:18:53
%S A059888 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 A059888 118,48,332,2,1436,6,448,54,222,88,7952,62,54,54,2680,6,698,30,476,
%U A059888 1476,222,14,7632,28,438,478,1916,14,1872,84,11896,118,58,14,784452
%N A059888 a(n) = |{m : multiplicative order of 6 mod m=n}|.
%C A059888 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 A059888 Also, number of primitive factors of 6^n - 1. - _Max Alekseyev_, May 03 2022
%H A059888 Max Alekseyev, <a href="/A059888/b059888.txt">Table of n, a(n) for n = 1..430</a>
%F A059888 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 A059888 with(numtheory):
%p A059888 a:= n-> add(mobius(n/d)*tau(6^d-1), d=divisors(n)):
%p A059888 seq(a(n), n=1..50); # _Alois P. Heinz_, Oct 12 2012
%t A059888 a[n_] := DivisorSum[n, MoebiusMu[n/#] * DivisorSigma[0, 6^#-1] &]; Array[a, 60] (* _Amiram Eldar_, Jan 25 2025 *)
%o A059888 (PARI) a(n) = sumdiv(n, d, moebius(n/d) * numdiv(6^d-1)); \\ _Amiram Eldar_, Jan 25 2025
%Y A059888 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 A059888 Column k=6 of A212957.
%Y A059888 Cf. A000005, A008683, A053449, A057955, A274907.
%K A059888 nonn
%O A059888 1,1
%A A059888 _Vladeta Jovovic_, Feb 06 2001