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

[Leroy Quet]

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.
%Y A138046 A138047
%O A138046 1
%K A138046 ,more,nonn,
%A A138046 Leroy Quet (qq-quet at mindspring.com),
Mar 02 2008

(Sequence A138047, by the way, is when
(d(n+1)-d(n))*(-1)^n is nonnegative.)


What I am wondering about is, just how fast is
this sequence expected to rise? What are its
asymptotics?
The inverse question: How many such integers n
are expected below a given positive integer M?

I bet there is something interesting here, but I
don't have the math background to know what it
is.

And, I might as well ask, I didn't miss a term or
make a dumb mistake when I figured this by hand,
did I? For all I know, the (correct version of
the) sequence could already be in the EIS.

Thanks,
Leroy Quet




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