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 A214701 #12 Jul 07 2015 16:37:14
%S A214701 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A214701 27,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
%U A214701 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66
%N A214701 Number of different values taken by sigma(k)/k for k from 1 up to n.
%C A214701 The first 26 values of sigma(n)/n are all different. a(28)= 27 since (6, 28) being the smallest friendly pair, 2=abundancy(28) already appeared before. When n belongs to A050973, then a(n) = a(n-1).
%H A214701 Michel Marcus, <a href="/A214701/b214701.txt">Table of n, a(n) for n = 1..1000</a>
%F A214701 a(n)/n tends to 0.98208.. approximately when n increases. - _Michel Marcus_, Jul 07 2015
%e A214701 a(2)= 2 because sigma(n)/n takes 2 different values up to 2 : 1 and 3/2.
%t A214701 s = {}; Table[s = Union[s, {DivisorSigma[1, n]/n}]; Length[s], {n, 100}] (* _T. D. Noe_, Jul 26 2012 *)
%K A214701 nonn
%O A214701 1,2
%A A214701 _Michel Marcus_, Jul 26 2012