When (d(n+1)-d(n))*(-1)^n is positive (d(n) = A000005(n))

[Leroy Quet]

--- Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

> I just submitted this:
> 
> %I A138046
> %S A138046 45,62,74,81
> %N A138046 Positive integers n such that
> (d(n+1) - d(n)) * (-1)^n is positive, where
>d(n) = the
> number of positive divisors of n.
>...


Okay. Maximilian Hasler has been kind enough to
calculate the first 999 terms.
He says that the plot looks almost like a
straight line over-all.
So I wonder, can we determine the limit, as n ->
infinity,
of a(n)/n?

a(999) = 7725.
So can we say that the limit is in the vicinity
of 7.7?
Maybe the straight-line-ness of the plot changes,
or the slope changes, however, for much bigger
n's.


Also, I have been thinking that it might be a
good idea to analyze this, instead of as one
sequence, as two different sequences.

(1) Odd n where d(n) > d(n+1).

(2) Even n where d(n+1)>d(n).

Are either of these sequences already in the EIS?

Thanks,
Leroy Quet




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