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 A059911 #15 Jan 26 2025 02:21:16
%S A059911 0,3,10,16,37,10,42,24,58,53,164,26,68,38,32,68,169,22,222,38,42,50,
%T A059911 328,40,180,219,108,26,334,82,460,82,92,72,220,108,449,86,128,80,192,
%U A059911 22,336,110,222,218,540,84,778,129,150,80,270,54,328,356,132,68,348,22
%N A059911 a(n) = |{m : multiplicative order of n mod m = 6}|.
%C A059911 The multiplicative order of a mod m, gcd(a,m) = 1, is the smallest natural number d for which a^d = 1 (mod m).
%F A059911 a(n) = tau(n^6-1)-tau(n^3-1)-tau(n^2-1)+tau(n-1), where tau(n) = number of divisors of n A000005. Generally, if b(n, r) = |{m : multiplicative order of n mod m = r}| then b(n, r) = Sum_{d|r} mu(d)*tau(n^(r/d)-1), where mu(n) = Moebius function A008683.
%e A059911 a(2) = |{9,21,63}| = 3, a(3) = |{7,14,28,52,56,91,104,182,364,728}| = 10, a(4) = |{13,35,39,45,65,91,105,117,195,273,315,455,585,819,1365,4095}| = 16,...
%t A059911 a[n_] := Total[{1, -1, -1, 1} * DivisorSigma[0, n^{6, 3, 2, 1} - 1]]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jan 25 2025*)
%o A059911 (PARI) a(n) = if(n == 1, 0, numdiv(n^6-1) - numdiv(n^3-1) - numdiv(n^2-1) + numdiv(n-1)); \\ _Amiram Eldar_, Jan 25 2025
%Y A059911 Cf. A059907-A059910, A059499, A059885-A059892, A002326, A053446-A053452, A002329, A055205, A048691, A048785.
%K A059911 easy,nonn
%O A059911 1,2
%A A059911 _Vladeta Jovovic_, Feb 08 2001