Average Of Changes Between Number Of Divisors

[Jack Brennen]

Leroy Quet wrote:
> What I wonder is, what is a(n)/n asymptotical
> towards?
> (This must be a well studied topic.)
> 

A little playing around with formulas gives:

   a(n) ~= n*log(n)+(log(n)*0.122-1)*(n*log(log(n)))


This formula comes within 1% of the actual value
for all n >= 10290 up to as far as I tested it.


It would seem to indicate that the ratio is asymptotic
to log(n), or perhaps more precisely, to:

   log(n)*(1+C*log(log(n)))

for some constant C.