Almost the number of divisors of n+1

[Thomas Baruchel]

Hi, I have some number-theory related empirically collected datas to study.
As long as I can see, I have a link between each integer and the number
of divisors of its successor. But though the rule seems to work very
well in some cases: predecessors of prime numbers seem to appear 0 or 1 times,
predecessors of numbers like 12 or 24 seem to appear much more, etc. I am not
sure this is the very exact rule. Of course, the trouble may come from
the fact that my datas is quite hard to "extract", but maybe you know some
variants of
   a(n) is the number of divisors of (n+1)
Have you ever seen closely-related sequences like that one?

Regards,

-- 
Thomas Baruchel