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 A337714 #10 Nov 23 2020 02:06:53 %S A337714 1,1,1,1,1,2,1,2,4,1,2,1,1,2,2,2,1,4,2,1,1,2,1,2,2,1,4,5,1,2,2,2,1,1, %T A337714 4,1,2,4,1,2,6,1,2,4,3,2,2,2,6,2,2,2,1,8,5,2,4,1,4,1,12,2,2,2,2,1,2,1, %U A337714 3,8,1,2,4,2,4,1 %N A337714 Euler totient function phi(N) divided by the multiplicative order of 3 modulo N, with N = N(n) = floor((3*n-1)/2), for n >= 1. %C A337714 For the multiplicative order of 3 modulo N = N(n), with N(n) = floor((3*n-1)/2) = A001651(n), see A053446(n), for n >= 1. %C A337714 For n >= 2 this sequence gives also the number of seeds s(N(n), i) needed to cover all numbers of the smallest positive restricted residue system (called RRS(N(n))) from the cycles obtained from s(N(n), i)*3^k (mod(N(n)), for k = 0..(P(N(n))-1), and certain s(N(n), i) chosen from RRS(N(n)). See A337936 for the choice of these seeds s(N, i). The cycles have period length P(N(n)) = A053446(n). For n = 1, N = 1, RRS(1) = [1] (not [0]) %C A337714 For the complete system of tripling sequences modulo N(n), for n >= 1, see A337936. %F A337714 Bisection: a(2*k+1) = phi(3*k+1)/A053446(2*k+1), a(2*k+2) = phi(3*k+2)/A053446(2*k+2), for k >= 0, where phi = A000010. %e A337714 The pairs [N(n),a(n)] begin, for n >= 1: %e A337714 [1, 1], [2, 1], [4, 1], [5, 1], [7, 1], [8, 2], [10, 1], [11, 2], [13, 4], [14, 1], [16, 2], [17, 1], [19, 1], [20, 2], [22, 2], [23, 2], [25, 1], [26, 4], [28, 2], [29, 1], [31, 1], [32, 2], [34, 1], [35, 2], [37, 2], [38, 1], [40, 4], [41, 5], [43, 1], [44, 2], ... %e A337714 The pairs [N(n)= floor((3*n-1)/2), P(N(n)) = A053446(n)] begin, for n >= 1: %e A337714 [1, 1], [2, 1], [4, 2], [5, 4], [7, 6], [8, 2], [10, 4], [11, 5], [13, 3], [14, 6], [16, 4], [17, 16], [19, 18], [20, 4], [22, 5], [23, 11], [25, 20], [26, 3], [28, 6], [29, 28], [31, 30], [32, 8], [34, 16], [35, 12], [37, 18], [38, 18], [40, 4], [41, 8], [43, 42], [44, 10], ... %t A337714 a[n_] := EulerPhi[(f = Floor[(3*n - 1)/2])] / MultiplicativeOrder[3, f]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2020 *) %o A337714 (PARI) a(n) = my(N=(3*n-1)\2); eulerphi(N)/znorder(Mod(3, N)); \\ _Michel Marcus_, Oct 22 2020 %Y A337714 Cf. A000010, A001651, A053446, A337936. %K A337714 nonn,easy %O A337714 1,6 %A A337714 _Wolfdieter Lang_, Oct 22 2020