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 A252594 #16 Dec 24 2014 23:00:38
%S A252594 1,2,8,16,27,32,54,64,100,128,200,243,256,400,486,500,512,800,972,
%T A252594 1000,1024,1600,1944,2000,2048,3200,3888,4000,4096,4624,6400,7776,
%U A252594 8000,8192,9248,12100,12500,12800,15552,16000,16384,18496,24200,25000,25600,31104,32000,32768,36992,48400,50000
%N A252594 Records in A072994.
%C A252594 Consider the function f(n) = the number of positive integers k < n such that k^n (mod n) == 1. This sequence lists the values of n at which f(n) reaches a new maximum.
%C A252594 All powers of two are present except its square. f(2^n) (with exception noted) = 2^(n-1) = 2^n/2.
%C A252594 All powers of two multiplied by 100, 1000 and 100000, but not 10000, are also present.
%C A252594 Terms other than the above are 27, 54, 243, 486, 500, 972, 1944, 3888, 4624, 7776, 9248, 12100, 12500, 15552, 18496, 24200, 25000, 31104, 36992, 48400, 50000, ..., .
%C A252594 Conjecture: f(x)/x -> 5/12.
%H A252594 Robert G. Wilson v, <a href="/A252594/b252594.txt">Table of n, a(n) for n = 1..94</a>
%t A252594 f[n_] := (d = If[ OddQ@ n, 1, 2]; d*Length@ Select[ Range[ n/d], PowerMod[#, n, n] == 1 &]); f[1] = 1; k = 1; mx = 0; lst = {}; While[k < 10000001, a = f@ k; If[a > mx, mx = a; AppendTo[lst, k]; Print[{a, k}]]; k++]; lst
%Y A252594 Cf. A072994.
%K A252594 nonn
%O A252594 1,2
%A A252594 _Robert G. Wilson v_, Dec 18 2014