%I #12 Jul 07 2015 16:37:14

%S 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 27,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,

%U 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66

%N Number of different values taken by sigma(k)/k for k from 1 up to n.

%C 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 Michel Marcus, <a href="/A214701/b214701.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n)/n tends to 0.98208.. approximately when n increases. - _Michel Marcus_, Jul 07 2015

%e a(2)= 2 because sigma(n)/n takes 2 different values up to 2 : 1 and 3/2.

%t s = {}; Table[s = Union[s, {DivisorSigma[1, n]/n}]; Length[s], {n, 100}] (* _T. D. Noe_, Jul 26 2012 *)

%K nonn

%O 1,2

%A _Michel Marcus_, Jul 26 2012