A214701 Number of different values taken by sigma(k)/k for k from 1 up to n.

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, 27, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66

Offset: 1

Author

Michel Marcus, Jul 26 2012

Keywords

• nonn

Comments

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).

Examples

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

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000

Programs

Mathematica

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

Formula

a(n)/n tends to 0.98208.. approximately when n increases. - Michel Marcus, Jul 07 2015