Missing mult keyword for possible multiplicative functions

[Mitchell Harris]

Following some recent musings on the seqfan mailing list, I decided to do
a search of the entire OEIS database, testing each sequence for being
multiplicative, and noting where the the keyword 'mult' is missing. The
test checked only the values, so it is necessary to check the meaning of
each sequence by hand in order to determine of the sequence really is
multiplicative.

Many of these sequences were obviously multiplicative. Such a list has
already been submitted.  But there are still quite a few for which I
haven't figured out (or taken the trouble to see) if they are
multiplicative.

The list is maintained at:

  http://lat.inf.tu-dresden.de/~harris/OEIS/mult.html

Many I still highly suspect are multiplicative (they often involve other
multiplicative functions) but would take more than trivial amount of work
(for me at least) to confirm and to give the multiplicative formula on
prime powers. Some of these should be totally obvious.

Suggestions:

- Find either the Dirichlet generating function (most likely involving
zeta(x)) or the version of the function on prime powers (i.e. a(p^e) =
(some function of the prime p, the exponent e, and any other needed
parameters) or even better, both!

- Check the sequence for info that might already be there (like the dgf or
a(p^e) or even a statement "This sequence is multiplicative").

- Some comments mention that the sequence is dependent only on the "prime
signature" (or something similar) which means that it is multiplicative.
If the comment does not give the full details of the function on prime
powers, try to fill them out.

- Some of the descriptions have constants that can easily be
generalized. Search the database for sequences that might already be
in there by generalizing the dgf or function on prime powers.  Then
fill in the gaps by submitting new sequences or comments to sequences
not listed here.

- for those that turn out not to be multiplicative (if it is otherwise 
very compelling that it is) please try to find a (smallest or easiest to 
verify) counterexample.

 To make things easier for Neil, please send the comments about
multiplicativity to me. I will collect them, update this page (so you can
see quickly where progress has been made), and periodically send the
needed changes (with individual attribution) to Neil en masse. Of course,
if you are creating new sequences, please send them directly to Neil.

-- 
Mitch Harris
Lehrstuhl fuer Automatentheorie, Fakultaet Informatik
Technische Universitaet Dresden, Deutschland
http://lat.inf.tu-dresden.de/~harris