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 A059909 #18 Jan 26 2025 02:22:07
%S A059909 0,2,6,4,12,4,26,18,14,6,24,12,64,8,16,8,66,20,36,8,64,24,76,6,28,12,
%T A059909 64,24,48,12,100,40,50,48,36,8,96,40,28,8,104,12,208,36,24,36,200,18,
%U A059909 48,36,36,24,128,8,152,16,172,24,48,12,48,36,56,72,40,8,128,56,48,40
%N A059909 a(n) = |{m : multiplicative order of n mod m = 4}|.
%C A059909 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 A059909 a(n) = tau(n^4-1)-tau(n^2-1), where tau(n) = number of divisors of n A000005. More 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 A059909 a(2) = |{5, 15}| = 2, a(3) = |{5, 10, 16, 20, 40, 80}| = 6, a(4) = |{17, 51, 85, 255}| = 4, a(5) = |{13, 16, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624}| = 12, ...
%t A059909 Table[DivisorSigma[0,n^4-1]-DivisorSigma[0,n^2-1],{n,70}] (* _Harvey P. Dale_, Nov 30 2011 *)
%o A059909 (PARI) a(n) = if(n == 1, 0, numdiv(n^4-1) - numdiv(n^2-1)); \\ _Amiram Eldar_, Jan 25 2025
%Y A059909 Cf. A059907, A059908, A059910-A059911, A059499, A059885-A059892, A002326, A053446-A053452, A002329, A055205, A048691, A048785.
%K A059909 easy,nonn
%O A059909 1,2
%A A059909 _Vladeta Jovovic_, Feb 08 2001